 You can convert it into one function by multiplying whatever is that number square. You can convert this to sin x or cos x. Completely, we can convert this part to sin x or cos x. In this case, all of you please listen to this carefully. This is one of the most important times you may get in school. In this case, use half-angle formulas of tan for this. We write y1 plus tan square x square 2 and we use cos x as and here 1 minus tan square x square 2 by 1 plus tan square x square 2. Now, please be very, don't forget this half. 6 square x square 2 dx is t. So, 6 square x by 2 dx will be 2. So, this is converted to 2 dt by minus t square plus 1. Now, after this, you know how the minus sign number 4 is 2 square. So, it will be 2 by 2 a plus x by a minus x. So, 1 2 1 2 goes off. So, it is half tan x by 2. So, tan x by 2 plus 2 minus root 3 minus tan x by 2 2 plus root 3. Do not mix and match too different. We will be nominated here in terms of cos x. Extend if I take it into a C and then I will have C. There is another thing, the C is absent. So, as Guru was pointing out, and now he is pointing out, we can convert this to a single sign or a cos function. So, there is a second approach, which I am going to show you now. But that works only when the C is absent. If C is absent, we could convert this to a single sign or a single cos function. So, in this case, if I multiply at 2, so I get 3 by 2 sin x plus half cos x. I can convert this to cos 5 by 6 minus x, isn't it? Which is integral of C 5 by 6, 5 by 6 minus x. Which is half ln mod C 5 by 6 minus x plus tan 5 by 6 minus x divided by minus 1, so it will become minus 0. Please note that the coefficient of x is minus 1, so it will be divided by minus 0. If you expand this, you will probably get this expression. So, both expressions are same. So, this approach can be realized that in the expression a sin x plus b cos x, C is absent. There is a constant term is not there. So, it is a special case that you can follow this. Now, if we requested one problem from the previous type, so we will take that one up and then we will move on to the other one. Is it done? Yes sir. Minus 1 by... Minus 1 by... Is that okay? You can do it. Coffee doesn't taste good sir. It should be here sir. Will you pop it or something? So, here what is the approach? Half angles in terms of times. Now, here I tell you what mistake people do. They forget to take the MCM. Sir, put that x by... That's the mistake. Another mistake is that they have 1 plus t square with that. They write 2t 1 minus t square plus 3. Okay. So, this 3 will be also 1 plus tan square x square. Okay. So, this will become 2 tan square x by 2. 2 tan square x by 2 plus 2 tan x plus 4. It was t... There is a 2t square. Cancel all the factor of 2. So, it's t square plus t plus... Now, I can apply the special... 7 by... 7 by... Huh? Yeah. Yeah. This is the very important thing for a school. Sir, how do you design a J question? We make a design. There you go. Shh! Integral of the time. Cos x in terms of tan and tan. Okay. I mean, I represent integration by parts. We express numerator and... Right, what do you mean? Oh, that would be... We ensure integration. That means... And this is the previous time. Yes, sir, correct. Huh? The moment I change the problem... I do, I do as you say. Okay. Example will make more sense. This is just a generic representation. Give an easy 6. Very... Very sin x plus 2 cos x plus 3. x plus 2 has 8 coefficients of sin x on both the sides. So, we don't have a sin x here. So, 0 will... Equate the coefficients of sin x on both the sides. A is minus 1, B is minus 2. Both the C is not that sin x. And equating the... A is 2B. Substitute over here. Which is minus. And C is... C is... Minus 8 by 5. Plus 2 cos x plus 3. So, divide it by... Divide it by sin x plus 2 cos x plus 3. Divide it by sin x plus 2 cos x. This is your problem already. 6x by 5 plus 3 by 5 is not as fine. It's just 2 cos. 2 cos x plus 3 minus 8 by 5. Please go to 1B. If R is... Let's discuss that. Not finish it up but you have most of the things. Sense time. You take it slowly.