 No panicking. So here we start and first question is for more are in single. No, you are you should be Start First question is on your screen and take your time and solve do not jump on do not jump on Solving or let's say, you know quickly finishing it. Take your time. Take your time Even if it takes a lot of time. No worries Okay, so take your time and solve Metaculously with pen and paper, right? Don't really try it in your mind Don't try in your mind again. I'm saying all of you have to focus on hundred percent accuracy I don't care about speed if you get on the first position Well, I'm good. No problem. But then if you are not getting it consistently there, that's a problem. So take your time and Solve and all all of you must solve and post your answer I will explain each question. So don't worry about the explanation part so Just and let's say someone is not able to understand In the interest of time, I would request the video will be there. Yes, 100 question 100 seconds The video is there After the session just take the video and look at the solution once again, okay? So for the interest of time, I will explain once definitely, okay? So here is the end and Yeah, so first Answer is okay. So a lot of lot of you have got the right answer. Many of you have not got the right answer. So Okay, never mind. So let me explain this and then we'll go to the leaderboard So it was very simple question the underlying concept was Complementary angles, isn't it? So complementary angles we have studied and that is what you have to you have to apply here So complimentary angle has to be Try now if you can join nothing like it try it. There's no restriction on anyone joining But if you are late, then it is a problem anyways So if theta and 2 theta minus 45 are acute angles such that sin theta is cos So convert sin into cos and compare the functions Compare the arguments you are done. What is sin theta guys sin theta is cos of cos of 90 minus theta Is it cos of 90 minus theta is sin theta? Okay, and this is equal to cos of 2 theta minus 45 degrees and that is what you needed to do Now you can equate the angle. So 90 minus theta is equal to 2 theta minus 45 degrees. So that is 3 theta is 135 degrees This implies theta is 45 degrees and you all know that tan 45 is 1 so This was the answer, right? This is the explanation to the first question and So you can just do q plus q2 whichever the underlying concept is the same. What is the underlying concept? All of you are using complementary angles so Complementary Complementary ratios of complementary angles is it and the basics basics were That sign of theta is equal to cos of 90 minus theta and vice versa tan theta was caught off 90 minus theta and vice versa and Second theta is cosecant 90 minus theta and vice versa Remember this Okay, this one, okay now Okay, understood any problem if any problem put an x otherwise, we will move ahead. Okay. So here is the first leaderboard Of the question so Dax from CHK very good. Keep it up. So let's go to the next problem guys. Okay. So here is the next Problem very simple once again, stay calm. Don't rush through Answers could be deceptive the options could be deceptive. So hence Just relax and Take your time. There's no hurry No, hurry. No hurry. What is that? Is 1 equals to a and b equals to 2 Hi, yes 1 a 1 2 3 4 is ABCD. Thanks for pointing 1 2 3 4 is ABCD. Take your time So this is again based on the same similar concept All of you should be very easily able to do it. Yeah Fair enough. So I think most of you have already Entered your answer Very good. This should be, you know, see Questions might appear to be little easier, but this is a very good mechanism of You know going through the concepts once again and revising all of that so Very good. So last 10 second guys. I think those who have not marked your answer. You can now mark your answer and complete the process Okay, so here is the last Three seconds and gone. So now let's check whether you have yeah, so most of you have got it correct And that's fine. I still find few people are either Doing it, you know deliberately in terms of let's say they're just marking it randomly. Don't do that so Explanation AB and CR interior angles of a triangle ABC then sign B plus C by 2 underlying concept So we'll write the underlying concept first and then solve it. So underlying concept is first of all triangle Angle some property of a triangle, right? So that you alert in ninth grade angle some property Angle some property will be required to solve this and the second thing which is required is again complimentary angles So knowledge of these two. Yeah, please Complementary angles All of these so a plus B plus C, you know is 180 degrees That means a plus B plus C by 2 Will be 90 degrees That means B plus C by 2 will be equal to 90 minus a by 2 Okay, so sign of B plus C by 2 will be equal to sign of 90 minus a by 2 and sign 90 minus theta is cos theta so cos A by 2 so someone who knows these two concepts will be able to Drive hope this point. Okay, so this is the option and most of you have done it correct those who haven't please take note of the solution and Do not repeat this again. So Where do you go? Yeah, so the updated leaderboard Very good. So the new leaderboard looks something like this very good. Why very good I'll get lunch aren't an up front of Alicia Namish, Surya, Shobita, Anish. Okay. No worries I don't really you know pay that much attention on this thing I will check your accuracy back end and that is more important to me. So hence again next question Stay calm 100% accuracy guys again 100% accuracy. Yeah Yeah, think about the question and then answer. Don't mark just like that Could be could be could be some trap Somewhere I think I have to check your internet dear. It's working elsewhere No problem. You can watch the quiz. No problem if you're technically not Able of attending it very good. Take your time People mark and then realize. Hey, this was something else and I did something else So that should not be the condition that should not be the thing Okay Quick most of you have This was again Never mind. Let me let all complete and then I'll explain Okay, so almost everyone has done so if everyone marks his answer we can Proceed to the you know the next step Right, so there are few more who are still thinking about it thinking about it Right, so this was ideal time taken for that should have been within 30 seconds But that's but then initial stages. Please take time. I'm no problem. Okay, so everyone has voted Anyway, so here is the answer guys So it was very very simple and most of you have got it correct. So good. Let me explain So it was fairly simple. Actually, this was you know Appearing to be complicated, but you had to just use underlying concept of again complimentary angles So complimentary angles E ratios right so sign of 81 degrees is simple cost of 90 degrees minus 81 degrees is it and tan of 81 degrees is part of 90 degrees minus Yeah, so caught 81 is caught 90 minus 9 degrees Sorry tan 81 it is right. Yeah, so tan 81 is caught off 90 minus 9 degrees. Am I right? No tan of 90 minus 9 degrees. My bad So tan of 99, right? So now what this is Sorry, yeah, so this is nothing but Yeah, so wait a minute Yes, so this is nothing but cost of 9 degrees and this is tan 90 minus 9 degrees for 9 degrees correct Right, so this was option 3 very very easy once again cost of or let's start from the beginning if you if you are Not comfortable to sign 81 and tan 81. No chatting now Right, let let the things be as it is so sign 81 can be written as sign of 90 degrees minus 9 degrees and This can be done as tan of 90 degrees minus 9 degrees both 81 word Right, and then what do you do sign 90 minus 9 is cost 9 degrees and tan 90 minus 9 is caught 9 degrees Very simple Okay, anyways. Yes, what's happening right? Don't worry. Okay, so here is next readable very good very good Nice to see lots of people coming up. Okay now any any difficulty Any difficulty anyone so if anyone has any difficulty again first step Second step third step. That's it. If you don't you know, just just mark. Just notice this. That's it Isn't it? Okay, next here, please take AC as 8 centimeter guys 8. It's not 6 So it's 8 centimeter AC is 8 again. I'm saying AC is 8 It AC is 8. So let me show you this so that it becomes easier. AC is 8 centimeter not 6. There is some slight mistake AC is 8 8 centimeter 8 centimeter AC is 8 centimeter. Don't take it as 6 Don't take it as 6 AC is 8 centimeter again re clarifying. Yes AC is 8 centimeter. Let me know. So AC is 8 centimeter. I think most of you have done it already Yes, 15 more seconds AC is 8. Please take care. There was slightly, you know typing error So inside clarified that 80 AC is 8 centimeter. Okay. Here is the time's up that the answer was See, right? So lots of you have bought it. Correct. This particular question has direct linkage with next year's Chapters on vectors and other other things. So it's very important to understand this So you now know area if you know Trinometry, you can find out area of a triangle. So This is the thing Right. So B was 90 degrees. So this is B. This is a is 30 degrees So let it be a and this is C and this was given as 8 centimeters Okay, so if it is 30 then quickly if you see this side This side will be 8 sine 30 degrees and this will be 8 cos 30 degrees So you have to be very very fast in this why because let's say this is why and this is X and this is H So clearly why by H is equal to sign 30 sign 30. So why is equal to H times sign 30? Okay, similarly if you see X will be H times cos 30 and then you know the area of a triangle Half into base into height. So base is X and Height is why so half into 8 into First X is cos 30 into 8 sine 30. This was the area Okay, so it's what is this half into let me write here. So half into 8 cos 30 is root 3 by 2 Sign and 8 sine 30 is root 3 by 2. These kind of questions will be typically asked in in case exam so, you know, so be ready for such things so hence is 2 2 and 2 this 8 will go and And So it is nothing but 8 8 root 3 Right centimeter square Right and third option is this option is correct Okay Fair enough. So, please remember. So if you also need to remember like that Let's say the formula now generally formula will be half into H square Hypotenuse square into Sine theta into cos theta whatever is the theta whether this theta or that theta the irrespective of whichever angle This is a formula for area of a Area of a triangle whose hypotenuse right angle triangle hypotenuse and one angle is given half H square sine theta cos theta in NTSC's Remember these formulae becomes very very effective. You were you'll be fast and you will be able to solve more number of problems Okay, great. So let's go back and check the leaderboard. So Right now the current status looks something like this Very good Keep keep the pace going very good guys. No problem. No problem. Okay, Shani is also there in the top 10 very good So we thought we really appreciate very good. Good guys. Let's move ahead and go to the next problem Take your time and then solve Take your time and then solve the top of a broken tree has it stopped touching the ground not figure is not shown I'll show it at a distance of 10 meters. This is the figure. Okay, so the figure was not coming over there So hence I have now shown it here So you can use this the top of a broken tree has it stopped touching the ground At a distance of 10 meters from the bottom if the angle made by the broken part with ground is 30 degrees Then the length of the broken part is so to find out the length of the broken part Take your time Don't mess with the ratios. Oh poor off. What is that? So don't mess with the ratios many a times in such questions. What happens is people Take sine cocosse secant copo secant and things like that. Don't do that So now I'm going back to the original question. So now, you know what the figure is. So here is question so Right, you should draw the figure quickly. So in NTS is let's say such questions come draw the figure quickly and Or let's say, you know, you can do it in the question paper itself if that's allowed So during our time, we were allowed to scribble on the question paper and we used to do that If it is allowed, you can just take the help of the figure given in the question itself and then you can solve No, it's in CBS. It's not allowed NTS. He is little different to you. Just check with them If that's allowed then you can do that Okay, very good. It saves time Right. Okay. Okay. So here is the Final. Okay. So 20 by root 3 Okay. Okay. So great. So, you know, so this is the Current or less is the answer and was very very simple actually very very simple So you have to find out the broken part. Let that broken part be H and The 10 meter anyways given so you don't need anything else. You just need to say cost 30 Was equal to 10 upon H simply and then done right So cost 30 was 10 upon H. So H would have been 10 upon cost of 30 degrees, right? And we know cost of 30 degrees root 3 by 2 that you should be very very thorough So don't forget it or don't mistake here or don't take you know commit any Is played late now can't really don't really know what is the problem Okay, so hence 20 by root 3. No worries guys You are learning. That's most important. It happens at Okay, okay. Yes, so hence hence I did I was pointing on pointing towards that only you will be knowing the answer You will be knowing the approach, but all this off, you know, I don't get me wrong But in all your minds right now it is there. How do I get on to that leaderboard or you know Hence that is creating all this the problem. So just relax. No need. Don't be in the leaderboard Anyways, I'm not going to judge anyone on this. So hence just chill and solve Okay, so here is the next leaderboard Result, okay. Good. Aditya's maintaining the lead. That's really nice. But then this time to shuffling No, no shuffling. Okay. Very good. Next question guys ready Yes Okay, fine. Shall we move ahead? Just five second pause all of you give me a thumbs up. Why all so far? So good any problem all good all good very good. So You're going good. Don't worry about the leaderboard. Just solve 100% correct. That's it. That should be the objective all even if you try only three all three should be correct. That's it Okay, next question Here is a question if x is a cos square theta Plus b sin square theta then so few people are just randomly marking it. I know That's really sad Take time and do it no hurry You're losing it if you're marking it If you're really fast and you have done it no problem, but then if not Then there's a problem. No problem area. What will what will go wrong? Take it? Let it go random Now the could you solve the problem? That's important. Could you solve it? Then fine be happy. No, why why do you care at times it might happen Or if you want you can re-log in or change the mode if you're able to solve that's that's good enough That's the agenda that means the objective is accomplished. So this leaderboard anyways How does it matter? Yeah, it gives you some kind of benchmarking against you all But hardly 70 people there are around I not less than four million people of your age Am I right? Yeah more than that in fact, but They will be writing different boards and total in India different board 10 graders, okay Here is the final This thing. So hence, let me see how many of you got it correct. Not bad. So at 28 people Uh, okay. No, no problem Kiran Mai and all, you know, so hence Uh, now let's let's analyze where did it go wrong? Why most of you could not solve it? How many of you got it correct? How many of you, you know Right, okay. So good Good. So let me show you it was very simple problem again So you have to just deploy the values and do it. So let's say x minus a Would have been what is x a cos square theta plus b sine square theta Right and then minus a Isn't it? So if you see what is this if you take a common you'll get cos square theta Minus one plus b sine square theta Right, which is a minus sine square theta Plus b Sine square theta. Why is it because one minus cos square theta is Sine square theta. So cos square theta minus one is minus sine square theta So that means now you can take Sine square theta common And you will get b minus a This is x minus a part. What is b minus x? So b minus x. Let's write so b minus a cos square theta plus Sorry, then it will be minus b sine square theta Okay, again take b common. So b common and this is one minus sine square theta minus a cos square theta So one minus sine square. All of you know is b cos square theta And this is minus a cos square theta So again, you can take cos square theta common and you'll get b minus a Isn't it? So now what was the question question was to multiply these x minus a and b minus x So x minus a is sine square theta times b minus a And the other part b minus x was cos square theta and b minus a Isn't it? So this is nothing but b minus a whole square sine square theta Cos square theta right and b minus a whole square is as good as a minus b whole square because squaring Doesn't impact the sine change So hence answer was What one b Right, I hope this is clear to everyone any problem here Any problem to anyone All clear any problem Right and if no problem Okay, fair enough. So that's that looks cool. And let's go back to our Yeah, so here is the updated leaderboard guys Well done very good. So question number six is done. We are exactly halfway through. Oh, so now there is some Suffolk. Oh good Nice. So there's a shuffle No problem. No problem. Yep, you know, uh, oh So sharduli was fastest in this one. Good sharduli. Keep it up next Next problem guys is your on is on your screen. Be careful again Now it will be intensive. You will require some kind of calculation. So hence People are so fast. They have just marked something, huh? guessing Most of you are guessing It is humanly impossible to mark it like that But you never mind. It's your call Okay, very good. Take your time and those who are seriously into it Take your time And then mark Marking is not required If you're not very sure Wait for it solve And then mark These are typical ntsc questions Typical comparative level questions. So they will not get to give you a straightforward one. You have to do a little bit of calculations Okay Very good. Take your time No hurry, but if you're marking it make sure that you get it 100% correct Syria get it correct That's it Yeah, very good So that means people are few people are really spending time. That's fine. Very good So lots of you have got it correct. Who could not get it any x here on a kid. Okay anyone else Good good. I will solve. Oh, what many of you? Okay, so now Here is the solution see if a cos cube theta there is a catch in this question I don't know if you would see the catch. There's a three here There's a three here And you know, there is a cos to the power one and two like that Isn't it? Okay I have just a minute Yeah, there was some issue in the question. I don't know how people have got it correct. There was some What is the issue in the question can anyone guess? Let me see if you're really smart those who have got it correct Who got it correct? Yes, where which which power luxe I didn't even know no problem which which power had an issue here Never mind We will cancel that question But which power which power had a had an issue over here anyone can tell me So in the second one cos square should not have been right? Yes So this shouldn't have in the second one. This should not have been the case. This two is creating a problem over here Yes, very good. Very good. So those who are honest, they could not solve It happened with me in my Inmo problem lots of people I have already told you that one question was wrong and it was only Required to prove that it was wrong Anyways, so hence are you guessed? Fair enough. So those who who could guess also Let's let's solve the problem first. So hence problem is if a cos cube theta plus 3a cos If you get such kind of problem in the exam then how to solve it and hence I was telling you the approach the approach was This was indicative enough. What was indicative enough this three and this three? Where have you seen this three? Yep, where have you seen this three? So this is this was indicative enough enough any never mind next was this was m Let me rewrite here so that I can get some more space to solve and then n was a sine cube theta and 3a cos This should be this rather the other way around Right, so this this two has to be there. This should not have been there This one This was the issue here actually. Yep. Okay. So why because if you add Let's say this question comes in NTSC this year So, what will you do add this and why do you need to add because see the question also They're asking you to add see it is indicative of that Right, so if you add you will get the trick. So if we add what will you get a cos cube theta plus 3a cos theta sine square theta plus 3a sine theta cos square theta plus a sine cube theta Now if you take a common yes, that was the catch correct correct stress So if you take a common it is nothing but cos theta plus sine theta whole cubed Okay, similarly if you see f m minus n would have been a cos theta minus sine theta whole cubed Correct. Now what you have to raise it to individually to two by three So if you raise it to two by three power m by n two by three will be what a two by three And cos theta Sorry, this is minus right so cos theta minus sine theta And two by three isn't it two by three and there was a three already Isn't it this is okay? I hope this is clear to everyone. So this is two don't get confused This is two by three. Is it fine with everyone? This is m minus n right? So this three and this three will go so it will become square term m plus n Hold to the power two by three would have been a two by three and cos theta plus sine theta Again three into two by three. So this three this three would have gone again And if you add both of them, this is what was required right add Add both of them LHS if you add what will be the RHS A two by three is anyways common to both the terms here also here also so I can take common And what is left within cos theta minus sine theta whole square will be cos square theta minus two cos theta sine theta Plus sine square theta. Is it it? This is the this term extension and this term extension will be plus cos square theta plus sine square theta plus two sine theta cos theta Isn't it so yes, so this one and this term gets cancelled sine square plus cos square will give you one And this cos square and sine square will give you another one. So that becomes two So answer should be two a Is the answer or the solution clear to everyone those who had raised x Okay, so there was Always women, let's say this this happens in the exam. What will you do? It could be possible And you know at the end of the day people are typing it somewhere, you know And it becomes monotonous at times to actually audit also So hence it might happen. Then what will you do? What will you do then in such cases in such cases where there is no way? Let's say there's not a subjective paper then do mark the answer Definitely mark the answer with whatever This thing you can think of so for example If you think that hey if this was two if this was this this two was not there It would make sense then do it because even if so what normally happens is What happened? No, no, no, so what happens is if there is a wrong question Marks are awarded only to those who have attempted In j e and all it happens Okay, if you don't attempt thinking that hey, you know Or because of lack of confidence or whatever Then you know, you might not get the chance because you haven't attempted it. Okay, so that's one thing So hence if you think okay, this should be like that and this should be the answer so mark it like that. Okay, no problem Fair enough. So let's go to question number next So No problem. I'm canceling the leaderboard here. So let's go to the next question NTSC no But in kvpy j e and all that. So quick Warming up everyone is like so fast here. Good. So super fast. No it was Uh, what do you say a question to warm you up in the middle of the session So that you can gain the confidence back. Okay, so Now everyone should mark it correct. See within 30 seconds. Everyone is done Everyone please mark it so that we can proceed to the next So the life will be like that and yeah, Aditya Ups and downs will be there So these are we you know, uh, see in Especially in these exams at least in the next year. It's not in NTSC that will be So in NTSC mostly what will happen or the other exams they will give you variation They will give you a variation, right It happens namesh at times. I there is there might be some bug here. See this server is in us Every everything is under lockdown. So you can have you know, we are able to use it I am really, you know, uh, thankful to that So don't worry about all that just Revise your concepts and make your fundamentals strong. That's the intention Yes, good. Okay. So, uh, uh, what will be the answer? Okay. Yes, here is the answer. It's all of you know it very easy. Oh, still some people That means they are Randomly marking it. So don't do that Yes, there will be but in this there was no catch Yes. Oh, why why that? Why that? This was so simple a question. You can see it and in fact the option also you didn't need to check So first itself was Uh, you know cos a is equal to 1 by secant a and then done Right. No problem No problem, right? So this itself is True. So hence never mind Is it? Uh Now you have to check for all the above but then all the above was not there in the option. No So this is clearly not correct This is a never possible Why sine is 1 by sine so how can that be 1 secant a corte is 1. No, not possible. Anyways Anyways, so fair enough. So let's go back and see the leaderboard now. Okay. So Change change change Okay I think namish missed that question and hence no problem. No problem. You are still there Good good good next question. Please here is the next Question It will not be that easy. So please please please take your time still. I see two people already marked it These people are start people Really good Some random guessing Take your time Okay, so where was that? This is a combination of two things There are two ways to solve it actually But definitely a combination of your knowledge of trigonometry as well as linear equations in two variables. So mixed Real life problems will always be mixed variety Real life problems will always be and you have to solve it in 90 seconds. I can see some people are still struggling. That's fine That means you are solving it Putting it putting more effort great really appreciate Really appreciate that's nice very good And here is the end of the show Right. Okay. So few people got it. Correct. Okay. That's nice appreciating Okay. So here how to solve guess Yes, at times, you know, so in the end. Yes, I'll explain So this was our question of linear equation as well as trigonometry So you have to solve for x and y guys. That was method one There is one more method even if you are guessing it could be a calculated Guess I will tell you. So if you see, uh, what is this? So you can say x is equal to y Uh y times a cos theta divided by b sin theta Isn't it This is x and let's deploy this in the next equation that is this one. So method of substitution for solving Linear equations. So hence if you now deploy a Into x and x was y into a into cos theta by b sin theta correct Is it so this is a into x and then there was a cos theta for this term as well here this term cos theta, right And then minus b y by sin theta And this is equal to a square minus b square. This will give you the value of y How so this cos theta and this cos theta will disappear very good So what next so let me simplify. So this is a square. So this a multiplied by this a will become a squared y by b sin theta Isn't it by b sin theta minus b y by sin theta and this is equal to a square minus b square Isn't it now What can you do? You can take the common denominator b sin theta Like that. So this will be a square y and this will be b square y and this is a square minus b square Correct. So y is common and a square minus b square will be there and this is b sin theta And this is equal to a square minus b square. Now you can cancel these two Right. So what is y dear friends y is b sin theta If y is b sin theta then what is x What was x anyways x was so hence x will be equal to y is b sin theta. So deploy b sin theta Into a by b sin theta times cos theta So this b sin theta b sin theta goes so x is a cos theta Right. So we I got x and y and what was the question question was to find out x square by a square. Let's find x square by a square. So x by a is cos theta And y by b was sin theta So y square by b square is equal to sin square theta And x square by a square is cos square theta. What will be there some? The sum is simply one, isn't it? So hence This was the answer Right Right and and you could have calculated the guess very easily. It could not be minus one. There are two squares over here How can sum of two square was minus one? So I eliminated Is it it so this is anyways eliminated Correct. Next you could have How could you eliminate this See there is something called dimension analysis dimensionally. So if you see there is no a and b term here In this Right. So there is similarly. There is no a and b term here. Right. So hence why would there be it is perfectly symmetrical You know expression. Why would there be any preference to cos and sin? So, right, this is also symmetrical. This is also symmetrical Why would there be one preference to x y or cos or sin? So this is also a one way of solving it Did you understand the symmetry case? So this is perfectly symmetrical. No x by a is equal to y by b and cos and sin Right. So there is no preference given over to x or y here. Also. This is perfectly symmetrical expression So why would this symmetrical thing Should have any preference of one particular t ratio. So all these are You know, so hence You could have taken that calculated guess This is when you are short of time and then you have to, you know, complete the paper. So this is called method of elimination Otherwise you could have done you could have just gone for You know, so you can see what should be the value of You know, so that it becomes c it is a something if you see this one a This one a Minus b and it is square square. So that means x cos theta becomes a then my job is done And y sin theta becomes b then the second equation will be satisfied. No Here it says I don't need to go formal way. I told you the formal way But in my exam I would have done like that. I can clearly see what do I see? I see there is a time something minus b time something and that is coming equal to a square minus b square If I just compare these two terms that is a x cos theta Is equal to a square. This is called trivial Solution method, right? So, you know, clearly if I put x equals to a cos theta and it gives me a hint that b is equal to Um, sorry y is equal to b sin theta and I check it here. It satisfies. That means I got it You can Maybe I don't know You never know your board board board is unpredictable. Anyways, so Why do you care? Now, you know you are equipped. Is it is it okay with everyone? Right, so let me see the new You need a board Okay, so Is again Yep, okay. Good next question quick solve it Hmm, let me see how many of you can do this Okay Take your time I really I really am proud of those people. You know you mark. You're sitting only for marking or what? Mark it. There's a there are four options. I will mark one. Okay This is also a good Take your time. You can't see the question. That's something reload reload. There will be a button to reload reload Still time is left reload Oh Never mind. Here is the question you have told me earlier itself within five seconds if the question doesn't appear Nevermind. I will I will now post it like that Okay So. Oh my god may very less the number of people have got it. Correct. Okay X one job or X X please X X X X X X X. Okay. Nevermind. So Now you are getting into the more. These are the typical questions guys. I'm telling you these are competitive level questions You will not get simple ones in the competitions. Anyways, so Fair enough what was to be found out x by y so find x by y. No, what is the problem, right? Oh, that was x Find x and find y Over so let's find x linear equations. I mean I'm not studied. So what is x here? So if you if you take this one and solve Yeah, so so if I cross multiply I'll get tan theta minus x cos phi x cos y tan theta Just correct me if I'm wrong One tan theta minus x cos phi tan theta is equal to x sine phi first equation Yes, right Okay, so hence what will happen so hence if you take x common so tan theta is equal to x common within brackets sine phi sine phi plus cos phi and theta right Never mind now now look at the solution. Don't worry about what happened. What happened now focus on whether you could solve this problem or not Okay, this will be typically a problem in NPCs at least so hence what will be x? x will be simply tan theta upon sine phi plus cos phi Times tan theta can be written as sine theta cost either Okay, so can I simplify this this will be And in fact, you know the numerator also is sine theta My cost theta that is tan and in the denominator. I can take common denominator. So it is cost theta sine phi plus Cos phi sine theta and divided by one cos theta So far so good Why is it is this board appearing to all Nice hello, who's that Aditi is it? You have to just re-log in dear Because you know, I think most of them are able to so never mind Not completely as in this full my My screen is not visible to you. Oh Okay, fair enough. So hence now you can just cancel this cost. So I got x as sine theta upon cos theta sine phi plus Cos phi sine theta. This was x This was x sir wrote on two things Yeah, so I'm right. This is my continuous canvas here. I Hope this is clear to me. It's my continuous canvas. I've just pasted the question over it. That's it. Okay Yeah, you need you don't need any kids sine theta plus five is not required So because you're not learned it you don't require now. Let's find out why So tan phi is why sine theta. Okay, so let me write it here. So I'm writing tan phi is why sine theta Why sine theta upon 1 minus y cos theta 1 minus y cos theta. This was tan phi. So let's find out why yes, it will cancel out. That's what so hence tan phi is tan phi multiply cross multiply y cos theta tan phi Is equal to why sine theta? So let's take why common so tan phi is equal to y common Sine theta plus cos theta tan phi Am I right if you? You know, so what is why why would be equal to tan phi? upon Sine theta plus cos theta tan phi Okay, and now again if you do this, what is it tan phi is sine phi upon cos phi divided by Sine theta and Plus cos theta Sine phi by cos phi Right. I'm doing a little fast. I Have never physically seen you and except for those you learn what oh again distraction now now this is Sine phi upon cos phi you need you guys need to do a lot of meditation you get distracted so easily Sine theta cos phi plus Cos theta sine phi whenever I look up for any problem in the chat and there is something else Cos phi, okay, so this is the thing now now Cancel right so hence what do you get y is equal to sine phi upon some simple mathematical Trinometric manipulation nothing else cos theta sine phi and my dear friend. What was the thing x upon y? What was to be found out x upon y you have to find out. Let's find out x upon y. This was x and where was why? This was why right? So let's bring both of them together. So x upon y is equal to sine theta upon Cos theta sine phi plus cos phi sine theta and Divide by y so divide by y will be sine theta cos phi plus cos theta sine phi divided by Sine phi am I right so this this goes so sine theta by sine phi is the right you get that All of you good that got it got it All of you got it how to So the solution who asked I showed the solution to you is how you have to so okay I'll tell you what to do You don't need to this is a lengthy question only Intimidating that's it. What you needed to do was express x in terms of theta and phi express y in terms of theta and phi and then This is divine Okay, so express x Yeah, so last step is this only so I expressed y in terms of theta and phi So I got this I express x in terms of theta and phi I got that so x by y will be simply this and thankfully my God's grace I had the same denominator, right? So while you are in the paper No, it's not that. Oh, that's what see why I if I would be solving this in the paper Do you think I will be writing all these steps not needed you know that the denominator and denominator is going to be cancelled Right, is there any shorter way? Yes, there is What would be that way? Okay, so What you can do is Take sign Take values the other way is Other ways take values So let's say you take there's no harm in taking phi as known value theta take phi as 90 degree Okay, take phi as 90 degree. So phi is equal to 90 degree. Let's say So now solve and theta will become what x upon 1 minus x cos 90 0 so 1 and theta is x Okay, okay, and the next is Uh, yeah, but then you'll have to be little. Yeah, so in this case, you'll have to have tan phi tan phi is And 90 is not defined. So you can't take phi is 90 to take some other value 45 maybe So you can your deploy values and do that from there as well. So take values So other way of doing it is in In the exam, you should do this what? And let's say tan theta theta is 45 or phi is 45. So what will be tan theta? And theta is x by root 2 and 1 minus x by root 2 this you have to do very fast, right? So what is tan theta? So pan theta is x upon root 2 minus x like that. And then what about this one tan phi is 1 Right tan phi is 1 phi is 45 degree. We had taken so one is so hence you'll get 1 minus y cos theta Is equal to Is equal to y sin theta? Okay, so what will you get as y? So y will be from this calculation y will be One upon sin theta plus cos theta so fast you have to do why is this what is x from here x is One and then yes one x is x times 1 plus tan theta is equal to root 2 and theta I will do calculations like that faster. So what is x? x is root 2 tan theta by 1 plus tan theta now check which one is valid Right like that you have to do so from here also you can get but then yeah, so you'll get one You have deployed this also so scientific root 2 value should also come here like that So you will get one of the options correct like this. Okay, so this is another way of You know if you're in there. No someone asked me Another one our techniques into my nobody's hey wait wait you understand So what I'm trying to say is in the exam I would have definitely gone through this method because and then I would have been I would have been a little faster here So I was doing it. No, no try and I wish is the one one of the methods because in the end at the end of the day You have to mark it correct. I would have definitely gone this way initially this way. Why because you know It will certainly give me the answer the other the thing was I was going slow here just to explain it to you If you are doing in the exam, you have to be super fast, you know And then you have to skip Steps without making mistake and that happens only when you have solved million questions Okay, so hence all these methods. I Will tell you more other method, you know informal methods of you know Let's say eliminating and all that stuff if you would have known let's say For example, what is time a plus be and things like that? Then you'd have done it much easier way. There are methods. Don't worry. Okay Okay, next let's quickly finish it guys. I want you to go home. Happy. Yep. So next question is Yeah No, I will not stress because that will be the you know, oh my god, lots of people could run any kid Got it correct. Very good. So that will be the You know The protocol you have to solve you have to develop this thing So the coach will never, you know lower down the standard. Then what is the point of doing all of that? Right, so please let us try to ace it ace it within 100 seconds period all of you and this is doable So you have to improve the yes 100 second What what did Gupta suggest later first question question question question come on complete it Let me see One more question to go. Come on. Pick. So those who are not able to see the question This is the question. I guess the values is it legal everything is fair in Competition and war now you're asking I tell you a story now that now that you have you know, so What is meant by honest police officer, you know What is meant by one honest police officer? Is there any term called honest police officer? So you it's like that, right? So you're asking like that. No, there is no police officers Must be honest by default. You need not attach a Honest to this thing is unfortunate that we have to say that it's like should do this he gave He was supposed to be shoes only why should there be a shoot the gay desi? Anyways, so we'll have a debate later on here Most of you have got it wrong and why is that? I don't know Aren't done. Oh, okay. Okay. Okay. Never mind. So so this was a mix of little bit of you know ninth grade identities problem and Trignometry and okay, let me let me show this to you. So sine x plus cosecant can be written as 1 upon sine x and This is 2 Okay, so what can I write? I can write sine square x Plus 1 by sine x is equal to 2 This was it could not have been easier than this. So hence sine square x Plus 1 is equal to 2 sine x What does it mean? It means sine square x minus 2 sine x Plus 1 is 0 Alright, so what is this sine x minus 1 whole square is 0. So sine x is equal to 1 So x is 90 degrees Correct now now put x equals to 90 degrees sine 90 is anyways one. So this is one Oh second 90 is one again. So this is also one. So one plus one is two. How much time was there required for this? So now you understand how the questions will be there will not be straightforward They will challenge your Was it so difficult? So if someone knew how to tackle this and It became an identity a square a square minus v square is Is equal a square minus 2 a b plus 1 equals to 0 from there you got sine square x sine x minus 1 is 0 So sine x is 1 sine x is 1 when when x is 90 degrees And you could have predicted like that also see sine x plus cosy cosy can't x is 2 So don't you think maximum value of sine x is anyways one Maximum value of sine x is how much one Right, so that means automatically cosecant x left would be one so when that when can that be possible? So you could have guessed the x value itself. Yes 90 degree directly. Yes, correct Rn. You could have done this x is 90 degrees Right, even if let's say x is some other degree, but it is definitely true for 90 So you could have just gone with that So if x is 90 sine x plus cosecant x is to that is that is this equation is satisfied Directly deploy 90 here and get the answer quick Right, so you don't need to do this formal way Let's say it was a subjective question. You could have done this, but it is an objective question You could have done like that Is understood by all right, so I could say you know only I was really disappointed this is very intelligent question But see only 22 out of those many Responded right so hence Both are correct in this grade normally you say 90 degree or pi by 2, but you don't require any There is no problem in taking 90 degrees or pi by 2 both are correct No, you will get the same answer next and the final question of the evening Or before that the leaderboard Okay, so oh my god, so many Good, so there is reshuffling. Okay. Cool. Next. So Monisha was fastest here. Monisha was fastest Okay, fair enough next question and the final one Take your time So there are a few people already What? Quality few will be ready to mark with my answer mark mark mark right now press. Yeah, one first person. Yeah, see This is so The hilarious at times. Okay, those who are not able to see the screen here is the question in bigger font Hey, this is not included. This is inclined. Sorry inclined if you have those who have knowledge of vectors can crack it in Five seconds different order. How can that be ABCD? What is a different order here on you get? Options will be in a B and C and D, right? It should be ascending instead of approaching who has created the question. Mr. Booker that is can you just capture the screen and Send it to me on a kid. I will just forward it to those developers What wait a minute. Oh, if you're already done, huh? The time is up Time is up. Is that time up? Okay? Not oh, I mean, I'll hear solver. Okay. So never mind those who have anyway, this is last question understand What is the value come on? How many if you bought it correct answer was one meter per second? How many if you bought it correct one meter per second? Those who had who are solved who have already done this vector thingy Would have understood this very easily question was this that there is a ladder This is the wall This is the ground This is the ladder and this is this angle is 30 degrees Making an angle of 30 degree with it A man is ascending the ladder at the rate of two meters per second. So he's going up two meter per second Okay, so the question was how How fast is approaching the wall? Right. So those who have done vectors, I will explain both, you know with vector It is like one minute. So the velocity was nothing but the component along with this Component of the velocity. So let's say this is the velocity or the speed of the man up upstairs or you know Guys and then this is 30 degrees. So this is 60 degrees. So the x component of velocity is the answer So we cost 60 Directly x component. Yes, yes, very good. So that means we into one by two So we was to answer will be one meter per second. This is for those who know vectors. Those who do not know vectors for them How to solve this Those who do not know vectors for them also. It is easy. Let's say The guy in one second the the person will travel two meter up agree Right in one second the person will travel two meter up. So he is going So let's let's let's try to find out one second scenario So in one second the guy has gone up two meters. Let's say this is two meters The question was how close he comes in that one second to the wall So let's say in one second the guy goes up to two meter and let's say he travels x meters towards the wall and This angle this was 30 degrees given anyways. So this is 60 degrees. So don't we know x by To is cost 60. Okay. So x is to cost 60 So if in one second he climbs up two meters, he will move towards the wall by X meters in the same one second that means two into two cost 60 is what? Two cost 60 is two into one by two, which is one, right? So if he moves, what does it mean? It means if he moves up by one meter He approaches the wall by sorry if he moves up by two meters in one second He will go one meter towards the wall in one second. So his feet towards the wall would be One meter per second. Is that clear? Give me why x and what why clear? Clear why all of you all of you, please? Otherwise, I like explain once again. Don't worry Don't worry. Those who want to leave can leave those who want to get more explanation can stay back Those who want to see the leaderboard can stay back Okay, fair enough. So hence I am taking and assuming that it is understood by all and here is the final. Oh Pranav well done. So you are the final winner okay, and Next was Aditya then Alisha from CHK Aniket. Good. Well done. Nana very good. Surya Monish Laksh and Neha. Well done guys. So you would have got your individual Performances in your respective accounts No problem Aditya. So hence be on time be on time everyone should be on time. So 805 is the maximum will wait Okay, no problem. Did you learn something today? The idea was to make you learn to give you a different perspective and to take you out Take you out from the common conventional methods and questions So you've got to you got some experience of Comparative level 10th grade trigonometry questions. Okay. So the next class mostly we will be doing what? What did we do linear equations? So let's do linear equations next Okay, good night folks. See you and Take care. Bye. Bye