 Good evening folks. Can you all hear me? Yeah, so you have to tell me if you can hear Hear me. Okay. Very good. So I can see lots of people responding now Okay, so welcome to the first mathematics and tomorrow guys. I hope Like last year we would be able to engage more and more with you and solve more problems Objective and some protocols as we have, you know friends from Batches where I don't really, you know, are I'm not very directly involved with them. So hence There is a protocol of the class Okay, no one first protocol. No chat. No discussion among yourself. So that's banned So I'm you know here That takes away a lot of bandwidth of the instructor. So it's Surya. No discussion. Okay So no one is going to discuss amongst yourself There's a provision that I can bar you from discussing amongst yourself But then I don't really want to do such kind of thing. So it's let's maintain the protocol Someone named iPhone. No, maybe they are. Yeah, so one request to all of you. Thanks Surya for highlighting that So now anyone who you feel is, you know, having some weird name Please highlight and the person and all of you have to identify yourself with the names that will be a mandatory thing because lots of unwarranted and, you know Illegal activities have been reported. So hence I would request all of you if you have any other name but your Name which you use in your school Please don't do that. Okay, by the way, just to tell you the technicalities of it every every bit of it is recorded including the IP address from your from where you are right now logged in and Every check of yours every click button click you do everything is received to us received by us in the form of a log Okay, so hence, you know, no worries. So if at all there is, you know, any Thing which is not legal or which is Immoral or whatever that's immediately recorded and we can trace To the IP address level so hence anyways, so this is what your information you must be Technically aware what all features are there every You know movement every activity whether you are not dating where you're talking to someone How many times you are, you know typing in the message box Then can you do it on moxa sir if it is ever going to be a fastest fingers first then can you do it on See moxa. We are trying to upgrade because there is we have a limit of number of people who can attend the session and Hence, we are doing it mostly. This is our Couple of classes on zoom and then we'll again go back to moxa because we have we are developing an integrated leaderboard in moxa itself. It will take some time But because of this corona issue everything has just been disrupted. But anyways Okay, folks, so we will start all of your, you know, those who are new with me in the session in the sense Those who do not know me. This is Tushar and I did mathematics and physics 9 10 11 10 12th. So I train for both subjects and now There's a protocol in the class wherein you have to say why when you know when you have to say, you know, say yes So just a demo why Why why why why all of you press why in your distinct? Yes Very good. So most of you know it already and if you have to say no, you have to say n like what we had in physics class So nnn is no no, right? And if you didn't understand anything you have to say what you know all what is that if you didn't understand anything Yes, very good. So I have to say x so so that we can Work on that particular problem now again likewise uncle. Have you joined the class uncle you're there So uncle sir is supposed to join because I will not be able to You know take this because you guys respond so fast that I lose track of who is saying what and become very difficult for me Just a minute So let me see if you can if I can manage that then I will do myself. Otherwise after some time Uncle sir will be here to take care of that. Okay, so I believe all the batches all the students who are here Have already done trigonometry. Just give me why confirmation why trigonometry is done by all Okay, great. Okay, great. Oh, I could figure out a way of Yeah, yeah, okay. Okay. Okay, fine. So now I can maintain a log as well just give me a second and I will get a um Little bit on your so that you can also see your performance Okay, so Let's see if we can do that. Just give me one moment So I will have now a leaderboard like that. Okay. Very good. So now start with sharing of the screen so sharing the screen with all of you and Let me arrange my screen like that. Okay. That's cool. And yes um, so here is the share screen option and I am sharing the screen with all of you fellas. Okay. I hope you can see the screen all of you Just give me a thumbs up if you can see the screen guys See the screen See the screen. Okay. Okay. Okay. Okay. Okay. So can you see a leaderboard also? So here I will type the name Yep, so that's what I'm going to do. Okay. So let's begin with the class so you know the rules you have question and then You cannot see leaderboard now. There's no nothing in leader. Oh, it's okay. Because I have not shared. Okay. Let me share the entire screen then wait so Share screen share Now I guess you can see the screen Can you see Can you see the leaderboard? Yeah, very good. So We will be jotting down All here. So we have to be patient because see your lots of people are there. I have to really You don't be a little faster anyways. Okay. So here's the first question We will be doing trigonometry today and let's see how many we can cover We will be doing 10th level stuff basics level and then we'll try to get a little bit of advance. So here comes the first question cos a is 4 upon 5 then the value of tan a is Right you have to answer in no, no, you have to answer in a b c d then otherwise I will not be able to Get it Yep. So, okay. Okay. Okay. Okay. Okay. Come on. Come on. Okay. So this is warming up game Warming up warming up. No problem warming up. Okay. So most of you have done it So let me see who has done it for the first this thing Okay, so I have the answer. Yes. I have the answer. I have First time stress. So hence the first answer today is from stress I hope this is stress from indra nagar. Right stress. Is this stress indra nagar? Yes, stress. Yes. Yes. So he is the first person then I have surya Who have responded correctly then you have a sharduli from k r m. So here is sharduli. So first then I have her shita and Aiden so these are the five people her shita Her shita and Aiden are the five people Okay, so the first leaderboard is here. Okay. Now next Format also. What is the format? What is the format? So I'm in tab take six tabs to get to chat. Please do in moxa next No, I'm okay. So you get into a pc. No Or if possible anyways, so anyone wants anyone who wants this answer say x Say x Anyone no one wants no one wants the answer. Oh, so cool. So that means all of your so cost a is four upon five It was a very very You know trivial question So if this is a this is for this is five cost a four upon five then tan a My Pythagoras term three. So tan is three by four, right? So answer b is correct So the first question is done going to send a question ready Ready ready. No, no no cross talk. Please. Okay. Next question is here So If sine a is half the value of cot a Is cot a is okay. Okay. Okay. So I have answers now Very good. Very good. Very good. So you have to mention question number. Also. Otherwise, I will I will lose track So to mention which question number Also So I have first our So his first entry is Then second entry is Surya again. So Surya gets a plus one. That means Okay, and then we have a ratchena. So that is a shit. I think so a shit gets an entry So a shit gets an entry and next is A nana gets an entry. So nana, right? So I have I think we I'm done. So nana. That's not Surya Yes, so one two three four and one more Pranav Jambur is the next person. So Okay, yeah, so this is Pranav J Okay, I think the screen is going on enough. Let me do some trick so that you guys are comfortable and I can I can always put it like that Yeah, now looks cool. And where is the Just give me a moment so that I can do this This is the score cut it from here and paste it in the start. Yes now. Yes very good and take it to here So that there is no flickering Sir, I answered before nana No problem. You are count. Who's who's who? What's your name? Shastanji Oh, you answered before nana. So never mind. So Sanjeev is also added. So Okay, great. Now, no problem guys. Anish Don't worry. It's okay. Try solving forget about typing answers. Okay. So answer is a All of you have correctly done is caught a sign a is half. So what is caught a caught a will be What is it caught a cost a Upon sign a these are all very trivial ones. So cost a is under root one minus sign square a Divide by sign a so you can do it from there. So one minus sign square a is one minus one by four like that So this is this is yes one by cost and then sign Sign is simply half. So hence you'll get root over three by two by one by two So root three. So hence answer is a so all of you got it. Correct. Okay. Very good. No problem No problem. Now, let's go to next level question number Yeah Do it Yes So answer answer has to be in terms of three a whatever three a vcd. Whatever you say like that Okay, keep keep writing keep writing So Okay, so here is what I have aditya k first So plus one then I have 3 s s so plus one Then I have laksh So laksh is new entrant laksh laksh Okay, laksh has got laksh has got one And then I have pranav. So plus one So hence one two three four and then us lesha is the new entrant. So us Lesha Us lesha is a new entrant. So here is the ush Okay, here is the so all the names plus one plus one plus one like that very good. Okay. So answer is 3b. Yes, correct 3b. How value of the expression course he can 75 plus theta. This is of complementary angles Complementary angles Okay, complementary angles Okay, so complementary angles say that the value of the expression cosecant Uh, 75 plus theta minus secant 15 minus theta minus tan and all that is zero. Why because cosecant cosecant 75 plus theta can be written as cosecant cosecant Or rather secant Secant 90 minus 75 plus theta Why because cosecant 90 minus theta secant theta and vice versa Okay, see I uh, whatever I am getting here as the this thing don't worry guys one once in a while it will happen Don't worry. So whatever I get I will take that. Okay. So anyway, so secant 90 minus Uh, 75 plus theta minus secant 15 be generous. You should be, you know, uh, giving you should be giving other Strong word it happens So you you will also get your chance. Don't worry. So secant 90 minus 75 plus theta secant 15 minus theta if you see this one and here this one will get cancelled, right? So they will become zero And exactly for the same reason this one and this one will be zero any x in this case Any x question number three any x anyone wants to Uh, and wants me to explain once again No, right any x no, okay, let's go to the third one the fourth one Given sine theta is a by b then cos theta is equal to oh x there is one attira and uh Okay, okay. So guys, yeah, you you please solve this and I'll attira and suman. I will come back to this So given that sine theta is a by b then cos theta is equal to many people are now responding Very good. So I have I have who all who all who all so I can see first answer I got for this Is from surya P Right surya p Surya is the new entrant. No, he's already there. So one becomes two And then I got from akshit such they are so akshit is here. So it becomes one plus then I got from Srishti so srishti is new entrance sris New entrant srishti. Okay. I got from srishti. Then I got from medha as well. Medha Medha Okay, great. And then I got it from aditya kumar nps ypr. So aditya Ypr I like just to Okay, so lot many people have done it. Wow. Very good. So these are the top five Okay. Now. So you missed me again. Oh, where is your name? Your name doesn't appear sanjeev So in my in my uh, this thing the first five people who got it are I'll I'll show you once again. Wait a minute. I have not received from you for me. It is For me the the ones which I have received. I'll read out the names once again. I have got Surya p then akshit such devas srishti sridhara medha and aditya kumar nps And sanjeev comes after mandunaths Jv, right? So sorry sanjeev. This is what I have received So yes, maybe the timing timing is Timing timing timing is something so your clock and my clock So let's go by this. There's no hard and fast this thing. You're doing good. No worries. So all of you have responded. The answer is c Uh, uh Answer is c. Did you all get yes answer is c and uh, how it's very easy So please listen to me very carefully sine theta is a by b Then cos theta is simply under root one minus sine square theta. So let me write it once again here So cos theta is under root one minus sine square theta. This is established identity. Why sine square theta plus cos square theta Is equal to one Okay, so from there under root one minus sine square theta will be one minus a square by b square Which is nothing but under root b square minus a square by b square, which is under root B square minus a square by b, right? So hence c is the answer any x in this case any x in this case Any x anyone didn't understand this please raise your hand or let me know otherwise Let's move on to for those who didn't understand three. I will come back to that. Okay, so let me just go ahead. Yes This is an interesting question is in cos alpha plus beta is zero then sine alpha minus beta can be reduced to answer is So so fast So fast Okay, so now I will ask the top five people who have answered this to explain this as well So so that I can you know, uh, yeah, I can listen from them also the first entrance here first entrant Was who let me just tell you So the first entrant is arian tundam. Can you unmute and explain arian? How did you solve this question? Arian, can you hear me? Yes, sir So first, uh, it's given that cos alpha beta is zero that gives us alpha plus 90 Alpha plus beta is 90 very good because cos 90 is zero. Yes arian go ahead Uh, then we used complementary angles. Okay That means, uh, this thing cos theta is like sine 90 minus theta So theta is like sine 90 minus theta. Yes Uh, so replacing like that we get sine 90 minus alpha minus beta sine 90 minus alpha minus beta Sorry, you are saying 90 is alpha plus beta So what should I write? I don't know what are you suggesting we need to do What should I write here? Because zero Yeah, what should I write? Zero I guess No, no, how see how did you get cos to beta? So a plus b is 90 Take your time. Take your time. Uh, so I will give a chance to next. Surya You answered it Now tell me how do you know this is to beta? Uh, or whatever it is. Yeah cost to be like unmute and explain Surya, can you hear me? Hello anyone Surya, can you hear me? Surya is No, not remembering and all is not allowed. No one will be now. I understood. Where are you getting the answers from now? You'll have to explain. Okay. So I nullify those those people who will not be able to explain Are out of the race. Okay. So don't this is not a guesswork guys. You have to Tell the right answer explain it properly No, so no remember. So next is next in line be ready. Who was that? So can I explain who's this? So Sanjeev. No Sanjeev wait wait for the you know, let me just first give the chance to those who have Answered correctly. So first was Then Surya then Pranav and Newton explain Pranav So, uh, we know alpha plus beta is 90 Okay So we can substitute alpha equals 90 minus beta Alpha is equal to 90 minus beta. Okay. So, uh, we know that they're given sine sine alpha minus beta Sine alpha minus beta. Yes Sine Hold on. Hold on. Wait. Wait Next Sambarudh unmute and explain next step Sambarudh, can you hear me? So I have Pranav then Sambarudh Then I had Akshit, Sanjeev and Pratik Shah. These are the people Right. So Sambarudh, do you hear me? Or I'm not able to see his chat. Anyways, what does Sambarudh say? Can he can he? Excuse me, sir. Yes. Who's this? This is Aryan Tendon sir. I can can I explain the next step, sir? Next next question next question. Okay. So, uh, then, um, uh, yes Akshit, can you unmute and explain? Next step Sir, sine 90 minus beta minus beta Okay, so I'm beta plus B So I have to replace alpha by this, right? Yeah. Okay. So you got Cost to beta. Yeah Very good cost to beta. Right. So this is how it has to be. You have you must be able to explain guys. So the point first goes to Pranav Pranav could explain so two and sorry two and then it is Sambarudh, I give you benefit of doubt. So Sambarudh, Sambarudh And then I had Sanjeev Akshit, Akshit was there. Akshit, Akshit is Akshit is two And then I'll give the benefit of doubt to Sanjeev and Pratiksha. San Sanjeev and Pratiksha Sir, it's already there. Sorry. Oh, Sanjeev is there. Sanjeev is there. Okay. Sanjeev is there. So Sanjeev becomes Yes. Okay. Good. Good. So you must be able to explain the answer. No problem. No problem. No problem. Next. Weird way. I mean it was Yeah, sorry. Style and error. Come again. It is Sarguli. Yes, sir. You have explained Sarguli. Yes. All new ways are welcome 10 points. If you have a New and different way, we can I will give you a wild card entry of 10 points. Thank you. Yeah, tell me. Cost 90 is zero. So I just took alpha and beta 45, 45. So I Yeah, so then you know, you can just take it as 45 and then you see that the sign alpha minus beta comes to be one So then you can say it's cost two beta and then No, I understand. But then alpha plus beta could be 30 plus 60 as well. No, Sarguli. So but then it would still work, right? Yeah, definitely. So if you are in an exam, please So anyway, we will be telling you that When in an exam Don't go by any formal method. The examiner or the evaluator just is looking for one of your choices. A, B, C, D He doesn't know whether you have done it by trick or by some shortcut or by some lengthy process doesn't matter You have to just get the answer for exam point of view. Yes, definitely But right now we will go by the formal methods and you know because alpha beta would be anything It could be 29 and 61 and things like that. So hence, okay Next This one is multiple times. You've done it What is it? six Oh my god, so many times people are Pranav is writing so many times. Okay Okay, let me just ask for the explanation then and then there will be a modification with five point bonus Okay, so on this question Oh, wait, wait, wait People who have typed first Aditya Viswanath enters Aditya. I will not want to ask you Aditya G I'll not ask Aditya Bajaj. I'll not ask stress and are in so all of you. I'm going to give it to you Because you guys have already. Yeah, so this is a very trivial one. So let me just first, you know, Aditya was the first person And then I have After Aditya Aditya is there Aditya. I have not mentioned your name. So Aditya G is there now G is the second person. Then I have Aditya Bajaj third person Aditya Bajaj is third and then you have stress stress is here. So one two And are in London are in are in are in. I was not there. So I will add are in here Very good. Very good. So he gets one point. Anyways, yeah So yes, so all of you now know this is the there is no, uh, you know, because why be because tan 45 is there. So, you know, tan one is equal to cot 89 degrees Right. Why because tan theta Is equal to cot 90 minus theta and vice versa cot theta Is equal to is equal to tan 90 minus theta. Very good. Very good for with that logic tan one and tan Right Right. So this will be there. This will go and you know kill each other. So one Centan two and tan 88 one tan three and tan 87 one But there will be one tan 45 in between also, which will be alone There is no pair up pairing up for this guy. So hence No, I I typed Aditya G Here is Aditya G. Aditya K is already there. Oh, I have twice. I've tried to take it twice. So here one plus Okay. Oh, so I have to write Aditya. Oh, sorry. Sorry. I I got my mistake. Aditya is here and Aditya K was one only. Yeah Never mind. Thanks for correcting Thanks for correcting. Okay. Now the variation to this is this. What is this value tan one degree tan two degree tan three degree tan 45 degree Not 45. So it will go to tan 45 multiplied by tan 90 degree answer What is the answer? Let me see who answers first Answer, answer, answer. Please keep answering. I am recording the answers And I'm I'm I'm recording the answers. I'm yes. Yes. Yes. Hold on those who have got zero And those who have got points ahead all so those who are saying it is zero. Let me just see Who all so we started with we started with We started with who first person just so many people are responding. Someone has answered seven also. That's good. Okay. So If I if I go back So if I go back, uh First answer lux lux says lux lux says Zero and he gets a minus five Okay, then pranav says undefined pranav gets one more. Where is pranav? So he gets three And then surya says zero. He gets minus five as well. Where is surya surya minus five dude Minus five. Okay. And then akshit satchadeva says zero akshit. Where is akshit minus five Okay, heavy penalty and then ishani ishani have you are the top five with minus five. Sorry Okay, so ishani has entered of five. So first five are done. Yes one two three four five Everyone else I can see anirudh saying zero shares saying zero shares also minus five Okay, who else who else aditi bhajaj minus five. Where is aditi? Aditi aditi aditi bhajaj is minus five. Okay minus five All of you will get minus five those who have said Right iron single minus five. All of you are minus five now pranav jambur. Very good minus five. Where is pranav? Pranav pranav. I I enjoy doing all this pranav. Where is pranav jambur? Pranav minus five. Okay. Now tell me why did you say Tell me why did you say Why did you say this zero Yes, surya. Yes, everyone those who are you know by mistake by mistake is disastrous Disasters, right? Right. So hence this is what you learn. So all these leaderboard leaderboard is at one place But you can't really you know No, so this is this is what the learning is don't really jump on you know seeing something which is very tempting Than 90 all of you know is undefined. So how can this number be defined right? So hence No infinity is not a right answer. It's undefined No infinity is not an answer Okay. Okay. Okay. Okay guys again. Hey, mr. Anizhut. Yep Yeah, do people who said not defined get points? Yes hardly so But you know, I will I I saw that you have you know said, you know plus one so hence but then Let it be like that. Okay, but you you got a punishment those who have said um Okay, so one more variation now When you are now answering this please be very very careful. Okay Never mind. Okay tan zero tan one tan two tan three dot dot dot dot tan 90 degree What is the answer? Yes. It's again not defined Again people are saying zero and all it's not defined guys see anything which is Multiplied by a not defined number. How can you get certainty? You know, so hence zero into not defined is not defined It's not defined. I don't know what it is. I don't know not defined only Okay, so hence I can't say what is this. Okay Fair enough. So be okay. Let me taste your Taste your patience one more. So the answer is not defined Not defined. Okay. So okay. Tell me this tan zero degree tan two degrees now tan two degrees. Okay tan four degrees dot dot dot tan 88 degrees Uh, what is the answer? What is the answer? Yeah, okay. Now this time you have got it. Correct. Yes, that is That is zero right because whatever is this value. I don't care till it is defined. That's fine And then multiplied by zero is zero So, no, this is a bonus question. You don't get a point on this. Okay. Next question guys. Here it is so the question is cost nine alpha is cost nine alpha Nandini, uh, you did understand that. Okay. So I'll explain to Nandini here. You can look at the board Nandini so, uh, you know, uh Yeah, so here is the here is the answer for the previous one tan zero degrees into tan two degrees Into tan four degrees and blah blah blah. Whatever it is tan 88 degrees. Let's say So whatever is this value? This is a finite value. I know there will be some value to it But tan zero is zero. So hence zero into any any finite value Finite value is zero Okay, so hence you got it. Yep great. Okay. Okay. Okay. Okay. Okay. So answer is people are saying seven is C. Correct. Okay. Let me see who all have done it. Seven C. A lot of people have already responded. Very good. Very good. Very good. Okay. So I get points and then question number akshit fachadeva is the first person. So akshit. Where is akshit? So you get akshit akshit akshit Where is it? Yeah, here it is. So you get one Three seven C. Okay. And Aditya G says no one is from Pranav Jambore C. Okay, Pranav Pranav you get one more. So four and then I have Sanjeev ten Sanjeev Sanjeev very Sanjeev Sanjeev. Yeah, Sanjeev is here. So two So three people done. Meeda Meeda gets one Meeda. Okay. And now I have one more aria Rao. So aria Rao gets new entry. Aria. Okay. One. Now I will ask who will who will explain you will explain Meeda Meeda unmute and explain how did you get C. Come on. Meeda can you hear me? Can you unmute and say Okay. Hello Meeda. So I can't I can do by chat. No problem. My name is vanished. Laksh. Laksh is there no. There is Laksh. Here is Laksh. You got minus five. Okay. Never mind. So next who can explain anyone. So Sanjeev you can unmute and explain. Yes. So here they have given that cost nine alpha is equal to sine alpha. Okay. So sir, cost nine alpha is going to be cost 90 degree minus alpha cost nine alpha is going to be sine 90 degrees minus alpha very good. No sir. Cost 90 degree minus alpha cost nine alpha is okay. I have have I written the first part correctly this one sir. Yes sir. Cost nine alpha is equal to sine alpha. Okay. Next. So its supplementary angle is equal to cost 90 degree minus alpha. Okay. So I just substituted cost there taking Meeda's common. So nine alpha is going to be 90 degree minus alpha. So 10 alpha is 90 degree. Alpha is going to be 90 degree. So there I took tan five alpha is equal to tan 45 nine into five and then tan 45 is one. So. Okay. Awesome. Very good. Right answer full marks minus five. Minus five is for those who have done blunder. Okay. Very, very easy. Question number eight. Fire. Fire. Okay. So I have here. Yeah. So I have first answer is coming from R N single and the answer is answer is correct. So R N is entering the rest R N R E N R E N is one. Okay. Next is coming from Aditya K. So Aditya K is here. He gets one more and then I think Aditya K no Aditya says answer is Aditya K. You are saying zero. You are saying zero. Okay. Yes. Yeah. Correct. Okay. R N Aditya Aden. Aden gets one. So Aden welcome Aden. So you get one. Then Laksh says A. So Laksh Laksh Laksh is here or Laksh had two earlier I believe and then minus five anyway. This is not going to compensate and then three now and then who has Pranav K P. This is new Pranav. So Pranav now K P. Okay. So yeah. So you got the entrance here. Okay. Very good. So 8 A is the answer is very. Yeah. It is very very. Oh, you are there. Never mind. We'll count it and nobody's. So Aden is there. So I can add one here and delete it in here. Yeah. Anyways, good. So it's very easy. Right angle at C then the value of cos A plus B. What is cos A plus B cos 90 degrees because A plus B right angle that C right so C is 90 by triangle sum 180. So A plus V is 90 degrees. So cos of 90 is zero. So hence you have now it's done. Okay. Never mind. Next question. Mind you love to explain. No, you have to answer in terms of ABCD guys. ABCD. So this is question number nine and yeah. So question number nine answer is question number nine. So first answer comes from Aditya G. Okay. So one then comes from Aditya Bajaj. Aditya Bajaj you get one now. Sorry. Minus five will be there. One. Then Aditya Bajaj. Pranav. Pranav Jambur. Where is Pranav? Pranav you get five. So now you are at zero after Pranav Aditya G. Hey Aditya you have written to twice. So one, two, three, one, two, three, four. Sanjeev. Sanjeev Sanjeev. Sanjeev. Where is Sanjeev? You get three. And then Harshita. Harshita is here. So she gets one. Okay. So right answer is right answer is yes I will explain sin A plus sin square. Who? Who? Okay. First of all I'll give this chance to Aditya G. Can you unmute and explain? Aditya G. Yes. So sin A plus sin square A is equal to one. Okay. So sin A is equal to one minus sin square A. So sin A is one minus sin square A. Very good. But one minus sin square A is equal to a cost square A. Very good. Those who didn't understand please note one minus sin square A is cost square A. Very good. Why is that? Because by the basic identity sin square A plus cost square A is one. Then. So sin A is equal to cost square A. So sin A is equal to cost square A. Very good. And sin square A is equal to cost power four A. Yes. So sin to the power two A is cost power four A. Okay. And from both the equations you get one. Yeah. So if you add this both these two equations one and two you add both you will get sin A plus sin squared A. Correct. Will be nothing but cost squared A plus cost to the power four A. Right. And we have we have been given that sin A plus sin square A here is one. So hence this is equal to one. So cost square A plus cost to the power four A is one. Okay. So one. So yep. All of you any x here understood. The answer is A. Anyone? Yeah. Very good. Next. Next. Yeah. Question number 10. Question number 10 guys. Another method is there. Okay. We'll listen to you. But wait. I just saw your message. So I have now from Surya. Question number 10. And he is saying it's D and Pranav also saying it's D. So Surya says D. And then Pranav also says D. Pranav Jambore. Here you have D. Then Aditi Bajaj says Aditi Bajaj says one more. And then I have Arya Rao. Arya Rao. Arya. You're there. Right. So two. So how many? One, two, three, four and Akshit. Akshit. Akshit. Where is Akshit? Arya Rao. Please explain. Unmute and explain please. Arya can you hear me? Hello. Arya, can you hear me? Arya. No, Arya, Arya, Arya. Arya Rao. Please unmute and explain. You can't hear me. Can you hear me? Arya. Never mind. So who's Surya? Explain. Surya P. Explain. Can you hear me? Guys, can you hear me? Hello. Yes, sir. Arya, please go ahead and explain. Sir, so sine alpha is equal to half. Yes. And cos beta is equal to half. Very good. By our normal trigonometric tables, we know that alpha is equal to 30 degrees. And beta is equal to 60 degrees. Therefore, 30 plus 60 will give us 90 and 10 degrees 90. Can there be any other method without using trigonometric table? Can you do that? Yes, sir. Who is this? Aryan Singhal. Yes, Aryan. Go ahead. Sir, you can use complementary angles. So cos beta is equal to sine 90 minus, yeah, cos beta is, yeah, sine 90 minus beta. And we know that cos beta is equal to sine alpha. Cos beta is equal to sine alpha. Yes. Now we can simply add t. Now we can, yeah. Yeah. So from here, you can compare the argument. So 90 minus beta is equal to alpha. So alpha plus beta is 90. So there are two ways. One was using the trigonometric table. Another was without. Good, Aryan. I gave you another method. Oh, another method. Who is this name, please? Exciting game. Locke. Locke. Locke, go ahead. So sine alpha and cos beta, they can only be equal when both alpha and beta are equal. So in an isosceles triangle. Not necessary. Not necessary, not necessary, Laksh. The sine alpha is half. Any way you said alpha is 30 and beta is 60. It happens only in this case. Sir, can we do like this? How? Explain. Okay. So sir, can we say half plus half is equal to one? So if we, oh. Yep, half plus half. So. Okay, we can. Sorry. All right. So there are two methods. There is one more method, which is called multiple angle. We learn in 11th grade. That also can be used, but then not now. It's not required. Okay. So great. Right. Okay. Understood. No problem. Okay. Let's go to the next one. So I have given the point for you. Okay. Here is it. Here it is. Sine one is 90 degrees. What? So first is, first answer coming from, I am getting so many answers here. So first answer is coming from Aditya K and he is saying answer is question 11. Answer is, Aditya, your answer is wrong, dude. Laksh Bharni. Answer is wrong. Medha Raj. Answer is wrong. Pranav Jambur. Answer is wrong. Most of you have done wrong. Why? First correct answer is coming from Aditya Viswanath. Good. Aditya is getting the first point here. That is two second point. Then I have got correct answer from Sanjeev. So Sanjeev, my dear, where are you? Here are you? So four. And then I am getting from Shobhita. Shobhita is new entry. So Shobhita is getting one. And then Aditya Bajaj gets another one. So good. And who else? So done. So Pranav, wrong. Aditya K, wrong. And then from Mo Amita. So Mo Amita is your first. Answer is B. And most of you have, most of you have done. Aditya Kumar NPS. You are saying X. I will explain. Don't worry. Okay. Many of you are saying X. Why it is X plus? Okay. Never mind. So let's break these into two parts. This one and this one. Okay. Yes. That was an add-on single RN. Don't worry. Now, so if you see sine square, 22 degrees. Let me explain. And sine square, who will explain this? I will give this chance. Who will explain? Anyone who wants to explain this? Aditya K. Aditya K is saying first. So let him explain. Aditya K, go ahead. Aditya, can you hear me? Hello, Aditya. I don't think he can hear me. Yes, Aditya Bajaj, go ahead. Next is. So we use complementary angles. We know sine square 22 degrees is equal to sine square 90 minus 22, which is cos square 68 degrees. 90 minus? 22. Hey, no. Sine square 22 is not sine square 90 minus 2. Cos square. That's how we write it in steps according to the book. Sine square 90. Included sine square 22 is equal to cos square 68, but in steps it's equal to this only. No. So anyways, wait a minute. Sine square 22 is not equal to here. Sine square 90 minus 22. This is wrong. Yes. So, but I don't know. I have a chapter in the book. No, you check. It will be sine. Cos square 90 minus 22. Okay, so. Any of them. Anyways, so hence, yes, go ahead. Go ahead. It's cos square 68 plus sine square 68. And similarly, the denominator also, it's sine square 68 plus cos square 68. Yes. So this is cos square 68, okay. Which basically, by using the identity, sine square theta plus cos square theta is 1. So it's one by one, right? Okay, hold on. Hold on. Hold on. So first part is rightly explained by her. So she's saying sine square 22 is anyways cos square 68. Why? Because sine of theta is nothing but cos of 90 minus theta. Okay, so that will give you sine square 22 as cos square 68 in the numerator. Now, if you see cos square 68 plus sine square 68 divided by again, if you do the same thing in the denominator, you'll get sine square 20. What's sine square 68 again, plus cos square 68, right? And this is nothing but cos square theta plus sine square theta is one. And in the denominator also, it will be one. So one by one is one. So this part is one. This part is one. Okay, what about this? Who will explain the second part? Sir, can I explain? Who's the first can I? R&N Pranam, Supra, R&N, I'll give you a chance. Yes, R&N, go ahead. So basically, again by complementary angles, we know that sine 27 is equal to cos 63. Amazing. Okay, so sine 27, guys, sine 27 is equal to cos of 90 minus 27, right? Yes, sir. 90 minus 63. Yeah, cos of 90 minus, no, that's correct. Yes, sir, 90 minus 63. So 90 minus 27. Yes, 90 minus 27. Yes, so that means cos of 63. Yeah, this is nothing but cos of 63 degrees, right? So replace sine 27 by cos of 63 degrees. So this sine of 27 will be gone and it will become what? Cos square 63. Sine square 63 plus cos square 63. And that is again one. One plus one. Two. So two parts, two ones, two, right? Those who could not understand, now it is clear to you. Give me a thumbs up. Why? Why, why? Give me a thumbs up. Those who asked. Yes. Okay, great. Great. Okay, hold on. No, no, no answering now. Next question is this. Question number 12. People are taking time in this. Oh my God, okay. So here is the first answer. First answer is here. So Aryan is the first Aryan Tandon. He's the first person who has answered. So Aryan Tandon gets one. Then Pranav Jambur is the second person who has answered. So Pranav gets one more. Then I have Anirudh Desai. Welcome. But Anirudh, what's your answer? You have written two. Which one should I take? Then Mehta comes, Mehta, Mehta, Mehta, Mehta, Mehta, Mehta is two. Then I have Laksh. Laksh, Varani, Laksh, where is Laksh? Laksh, here he is. So yep. And then I have one more. Laksh ke baad. Harshita. I got Harshita here. Harshita one. Right. So I have Pranav Sanjeev is also there. What did I do? Aryan Pranav Sanjeev. Oh Sanjeev was also there. Pranav Sanjeev. Pranav Sanjeev. Sanjeev, Sanjeev, Sanjeev. My word. So many people are now included here. So I am losing the track. Okay. Yes. Okay. Yeah. Sir, mine becomes two. Yeah. Harshita are two. Okay. Yes. Okay. Very good. C is the answer. Who can explain? Who will explain? Can I explain? Who's can? This is Aryan Tandon, sir. Aryan Tandon. Yes, you had a lost opportunity. So explain. Sir, in this question, we'll divide the numerator and denominator by cos theta, sir. Right. Very good. So dividing numerator and dividing nr and dr by cos of theta. Yes. So what will happen? Sir, we'll get fourth and fourth and theta minus one and fourth and theta plus one. So let me write the steps so that those who are not able to understand will get the view cos theta. So I am dividing the numerator as well as denominator as suggested by Aryan by cos theta. Okay. Here then this is cos theta by cos theta. So now it's a matter of simplification. So this is four times tan theta minus one divided by four of tan theta plus one. Why? Because sine by cos is tan. Next, my dear. Aryan, go ahead. It's given in the question that four tan theta is three. So we'll get three minus one and three plus one. Yeah. So four tan theta is three. So you'll get, okay. So four tan theta directly, you can, you know, four tan theta value is given to you. That is three from here. So write three minus one by three plus one. Sorry. What? Yeah. Three plus one. So hence it is one upon or two upon four. Two. Very good. Right. Nice. So Aryan single another method. Aryan will get two points for another method. Go ahead. Aryan, another method if you have. So basically, one by one, one by one, everyone will get a chance. Yes. Yes. Go ahead. Aryan. So four tan theta is equal to three. So that implies that tan theta is equal to three by four. Okay. So using Pythagorean triplets, you can find out that the hypotenuse is five. So you know the value of sin theta and cos theta and then you can substitute and calculate. Yes. But I would, I would ask you not to go to Pythagorean serum anymore in trigonometry. Please use identities to solve such questions. Okay. You can do that. There's no wrong in it. You'll get marks and all that. But then that is like leave these kind of things for eight and nine graders. Now you are in 10th grade. So you will use identities. You play with identities. Okay. Aditya has another method. Aditya, go ahead and tell me. Aditya, you have another method or the same method? Anyone else has any other method? No. Same. Okay. I have another method. Four. I have another method. Let me show you that method. There you go. Four tan theta is equal to three. Right? So it will be four sin theta by cos theta is equal to three. That means four sin theta is equal to three cos theta. I will use this. Where? So if you see the numerator is four sin theta minus cos theta, that means three cos theta minus cos theta. It's the same thing, but then different way of doing it. And then three cos theta plus cos theta, isn't it? Because four sin theta was three sin theta. So hence if you see this is two cos theta by four cos theta. And if cos theta is not zero, you can eliminate cos. So you'll get one by two. Okay. Is there any other method? Is there any other method? No method. Right? Very good. So 12 done. Question number 13. Do this. 13. Question number 13. But you don't need to calculate what hyper because it cancels in numerator and denominator. Anyways, from, yeah. So hence I'm getting the first answer. First answer is from, now who's that? First answer is question, Nandini is asking for question 12. Okay. So here is question 12, Nandini. By the way, I will give the points now to, Momita says, Momita, your answer is wrong. Pregival answer is wrong. All of you are wrong. Wait a minute. Nandini, is this okay? Yes, sir. You can change. Thank you. Great. So all of you are going in the wrong direction, my friend. All of you. Why is that? Yeah. One answer is there. I can see one, one answer, which is Sharduli you have done. I think, wait. Yes. So I can see only Sharduli coming up with the right answer. All the answers are wrong. All the, okay. I didn't, yes, two points. Sorry. I didn't get two points for explaining, but then I thought it was, it will be a different method. But anyways, I had promised while giving you two. Don't worry. Okay. Nyanesh, me. Yes, Nyanesh. You also, now you have changed the answer. Now people have changed the answer. So only Sharduli will get because all of you have. So who had said, okay. So next was Nyanesh. Yes. Nyanesh and Nitya. Okay. And Aditya, no wrong. So hence I have new entry. Nyanesh. Nyanesh and Nitya. And Aditya, no wrong answer. Then Nana. Nana is new entry. Nana gets one. Nana. Nana gets one. So four people and one more I'm looking for Nana. And Aditya K. Okay. Aditya K. Where is Aditya K? Here it is. So three. Yeah. These people have got it. Okay. So all of you are saying A. Sharon also, but sorry, dear. You just missed it by one. One, you know, yeah. Oh, you're already there. Nana, you're there. Nana is there. Oh, yes, she's there. So one. Okay. Never mind. Lots of people are now there. So hence. Okay. Okay. Yeah. So hence. Right. Okay. Never mind. Those who have missed, you have not. Lots of points. So now if sin theta minus cos theta is zero, then the value of sin square. This was very, very simple question. I don't know why did you make mistake? So yes, I know. Wait, anyone else wants to explain this question? Anyone? Who's can I first? Can I was? Shaduli. Yes, sir. Okay. Shaduli, go ahead. Okay. So, um, we know sine 45 is one by root two and cost 45 is also one by root two. So one, so sine 45 is equal to cost 45. So theta like, so it's one by root two. So sine, uh, so one by root two raised to the power four is one by four. Plus again, one by four is two by four, which is one by two. Okay. So very good. So you are saying you, you are going in the reverse, this thing. Yeah. So cause sin theta minus cost theta is zero only when theta is 45. Can sin theta and cost theta zero also in other case, can there be another possibly another possible value of theta where sin theta and cost theta zero 135. Yes. 135. So hence, you know, uh, Shaduli, uh, the, you know, best method, best, yes, there is 135 degree. No, not 135. Sorry. Who said 135? That's wrong. Now, sin theta minus cost theta is equal to zero and not at 135, 135, 225. Yes. 225. Right. It will be in third quadrant, 225 degree, 225 degrees also. So hence, don't go by deputation of values over there. Instead of that, anyone else has any other method? So, but value of 225 will also be one by root two, right? That's okay. But I'm saying, but there are so many theta values where you will get sin theta minus cost theta is zero. For example, 360 plus 45, that is four, not five degree. Again, it will be zero. Then add four, not five and 180 to eight. So 225 plus 360 sin theta minus cost theta will again be zero. There are lots of values of theta where sin theta minus cost theta is zero. Okay. So anyone has any other method? Ariane, Tandon. Go ahead. Go ahead. Sir, in the given equation, will square both sides, sir? No. No, no, no, don't square. Squaring leads to loss of roots. So, Aselesha, what I was saying is there are lots of values of theta where sin theta minus cost theta is zero, right? Lots of values of theta. What, what values? So here is 45 degrees. So here definitely one. And then you come full circle again. Again, it will be zero. You come full circle again. Again, it will be zero. So lots of thetas are there. So don't put, don't solve these kind of questions by deploying values in, in a, in a, in a comparative exam, please do whatever some dumb done the way you can apply to solve. But then we are here to build the concept. And the formal way of doing it would be that can I say sin theta is equal to cost theta, guys? Yes, sir. And then sin theta by cost theta is 1. So sin theta divided by cost theta is 1. So tan theta is 1. So tan theta is 1. So tan 45 is 1. Now let's say I don't want to get into this degree theory stuff at all. You know, I don't want to get into numbers. Can I still solve it? That's the catch. Can I still solve it? Can I still solve it? No, you can divide it by cost to the power 4 theta. So I will get a cost 4 anyways in the numerator. Yes, squaring is okay, but then I will try to avoid it. Can I, you know, if tan theta is 1, can I find the value of sin square theta, sin 4 theta plus cost per theta? Look, without going into the value system. Okay, then, okay. So you are saying divide the whole thing by cost 4 theta. So sin 4 theta divided by cost 4 theta plus 1. But then I will also have one cost 4 theta here, is it it? So you will get tan 4 theta plus 1 into cost 4 theta. Now what do we do? Sir? Yes. Sir, can you say that if tan theta is 1, tan square theta minus tan square theta is equal to 1. Very good. So you can say x square theta is 2. So then sin, then root of that will become 1 by root 2 and then you can substitute that. Very good, very good. So hence, the next step will be here. So what I'll do is tan 4 anyways, I know tan kawaliu is 1. So 1 plus 1, right? 1 to the power 4 is 1 plus 1. Cost 4, can I not write it as 1 upon secant 4, right? And then it is 2 into 1 upon secant is, right, secant square, secant square, square. Can I write like that? Can I write like that? Then this is 2 into 1 upon secant square is 1 plus tan square theta square is in t, right? So hence, what is, since we see this is 2 into 1 upon 1 plus 1 whole square, right? Because tan square, tan was 1. So hence it is 2 into 1 upon 4, which is 1 upon 2. I never got only into this theta business, what is the value and all that. You can definitely do it, but there is another way of finding the same thing without getting into the business off. What if tan theta was not 1 and something else? Let's say, you know, sin theta minus cos theta, if I would have, instead of giving you 0, if let's say I would have given you this, that sin theta, sin theta minus cos theta is let's say 0.5, okay? Could be possible, right? Sin theta minus cos theta is 0.5, then what will you do? Then becomes very difficult to solve or instead of that, let's say this is anyway difficult for, at this level, what I'm saying is, let's say if I would have given you sin theta minus 0.5 sin theta is equal to 0. This kind of a relation, if I would have given you, then how would you solve it? So then you again come like that, sin theta is equal to 0.5 cos theta and then divide by sin theta by cos theta is equal to half. Now here is again, thankfully it is half so you know, no, but then this is tan theta. So tan theta is half, you don't know the value of the angle. So how will you solve it? Is it impossible to solve now? Why are we making it difficult, madam? We are making it difficult because life is going to be difficult later on. So hence, in the question, you will get 0.5 and the heaven will come crashing down. So hence, be ready for all the different approaches of the same problem. So let's say tomorrow in the exam you are getting this instead of sin theta minus cos theta. So learn varieties, how to attempt and solve such problems also. Is that clear? Give me thumbs up. If all of you are clear on this, there are a few harder questions which we could not do today. Never mind. It is first centymar of ours. So later on again we'll proceed. We'll spend one more. So be ready with all your basics. Next centymar in maths is going to be level two. So today it is a warming up session. Next session will be difficult one. So hence, your average number of questions solved per hour will go down. So come prepared guys. So the result of today is this thing. As a first this thing, I am pardoning all of you. So I am deleting this minus five thingy. So don't do this mistake again. So minus five is gone. This minus five is three. So this minus five is one. So hence, all of you are nothing but this is the final tally. So who is the winner? So I have Pranav. So you deleted my plus two. I deleted your plus two. So let's say Rn is three now. Okay. So first one Pranav. Bold. Okay. Second. Who is there? I can see Sanjeev is there. Okay. Very good. Keep it up. Then we have fourth place Akshit. Akshit is there. Akshit is there. And then we have Laksh there. Okay. These are joint third and lots of three. So Surya is three. Aditya K is three. Then we have Aditi B. Pajaj is three. Rn also three. But you have got a bonus. Okay. Right. Okay, guys. Bye. So, okay. So hence, can you repeat 14? Yes, I will. Those who want to, you know, get more clarity, please stay back. 14. I have not touched 14. Sai Rishita, I have not touched 14 or 13. Okay. Yes. Here it is. So it is given that sine theta minus cos theta is zero. So let me explain. Sine theta minus cos theta is zero. Right. So I can say sine theta is equal to cos theta. Right. So that means tan theta is equal to one. Why? Because this can be written as sine theta upon cos theta is equal to one. Right. What happened? Yep. Okay. Okay. Okay. Bye. Who's who asked this question? I lost the message only asked from Rishita. Okay. Yep. Rishita. Okay. Now, so if tan theta is one here, then one attempt was that tan theta is equal to tan 45 because tan 45 is one. Okay. So in your grade, you can do that. So theta is 45 degrees. So now if theta is 45, then put sine four and cos four question was find the value of sine four theta plus cos four theta. So put the values cos of 45 degrees four plus sine of 45 degrees to the power four. Now cos 45 is one by root two. So one by root two to the power four plus one by root two to the power four will be equal to one by two plus one by two. Is it? Sorry. One by four plus one by four. Sorry. One by four plus one by four and this will be one by two. Rishita. Is this clear? Is this clear? Rishita. Just respond. Yep. Anyone? Anyone else? Anyone else? Anyone else? Anyone else? Any other question? Please stay back. Any other doubt? Anything? Please clarify. Okay. Please clarify. Okay. Can you explain the other method to one with secant? Yeah. So hence, other method was I am not going into this. I will start from tan theta is equal to one. Okay. So secant square theta will be what? One plus tan square theta by the identity which we have learned. So this will be two because tan theta was one. Isn't it? Secant square theta is equal to one plus tan square theta and tan square was one. So two. So that means I have to find out. I have to find out sine four theta plus cos to the power four theta. Many people said sir divide and multiply by cos four theta. So I multiply by cos four and divide by cos four. So it will become sine four theta upon cos four theta plus one. Right. So now I can say cos to the power four theta is one upon secant to the power four theta. And this is nothing but tan to the power four theta plus one. So the answer for the sine theta minus cos theta is half. Yes. You can find that out. No problem. Now you know the method. So one by secant four is can be written as secant square theta whole square and tan four theta will be nothing but tan theta to the power four. No plus one. Now this is one upon secant square. Secant square value was two. So I can write this two squared. Okay. And this was nothing but one plus one because tan was tan theta was one. So one to the power four is one. Then plus one is so hence it is one upon four into two. So half. Got it. Yes. Any other question guys? Any other question? Okay. Any other question? No. So then we'll stop here and thanks for coming to this session. Next centaur as I told you will be level two. So don't get disheartened if you score very less. It is deliberately made difficult. So hence let's see how do you fare. Take time but do well. Right. So that will be level two guys. Okay. Come prepared. Bye. Take care. What is please. Sir, could you repeat that thing? Whatever you said about tomorrow's session. I just logged out by mistake. Tomorrow's session. There is nothing tomorrow. Day after no day after will be some other subject. Whenever the next centaur is for you it will be level two. Level two of trigonometry. So today was level one. Now we'll step up and we'll go to level two. We'll go to level two. Okay guys. Bye. Take care. Bye. Bye sir. Bye. Take care.