5

11) 10) Simplify h tan8 _ cot B 1 sina tana + A) sec 0 ] the expresaion: cOS 4 tan 0B) 1 +2 cos2B) cos 4cOs 0 sin 00121D) csc aD) 1 - 2 cos2sin2...

Question

11) 10) Simplify h tan8 _ cot B 1 sina tana + A) sec 0 ] the expresaion: cOS 4 tan 0B) 1 +2 cos2B) cos 4cOs 0 sin 00121D) csc aD) 1 - 2 cos2sin2

11) 10) Simplify h tan8 _ cot B 1 sina tana + A) sec 0 ] the expresaion: cOS 4 tan 0 B) 1 +2 cos2 B) cos 4 cOs 0 sin 0 01 2 1 D) csc a D) 1 - 2 cos2 sin2



Answers

The expression $\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}$ can be written as $[\mathbf{2 0 1 3}]$ (A) $\sec A \operatorname{cosec} A+1$ (B) $\tan A+\cot A$ (C) $\sec A+\operatorname{cosec} A$ (D) $\sin A \cos A+1$

So here we need to prove that our alleges is equal to our marriages. Okay Our alleges is one plus card a place turn a into sign of a minus cause of pain. And our marriages here is set a by because ex choir a minus Kazakh vibe. Sex square eight. Okay so as usual we will again start with our NHS here. Okay you can start between the side. It does not make a difference. So let's begin. Like I always say first convert all of your known terms in terms of sine and costs. Okay they are our friendly towns. So cause by sign of a class sign of a by cause of eight in two years we have signed a minus cause a no taking calcium in the first record you always have sign it into cost. So you already have signed a less cause a okay and then the denominator will have you uh yeah I was a sine squared decor squaring and yeah we would have signed A. R. A. Okay. Yeah, we have signed a minus because of it. So now you open this cracker to make it a little bigger. So this will look like sign a minus cause of into. We have signed square. Let's go square a less sign a course and then sold by the advice to cause of the Okay. Now, if you look at this carefully, the numerator is a Q minus V cube which is equal to a minus B squared plus b squared plus 80. All right. So this will look something like this say cube minus house cube of A. There are advice signed a crossing no separating the numerator and denominator. Yeah, we have signed cube by plus minus here. We have prosecuted. You know, we have sunny egg toss it. All right. So this will give me Cancellelling one sign and then sign here and one cause and one cause here. Yeah. So you're remains to your also remains to now, what is the universe? Of course, this is a What is the inverse of science or, you know, we have. Does that square party than words of sign here? This will be closed. And there was, of course, will be six square which is equal to our marriages. Hence, through if you have any further doubts, please feel free to let me know. I'll be very happy to help. Thank you.

So the question here is to again prove that LHs is equal to our NHS Alright, what is our alleges? Our alleges is one minus Kosek minus card A minus one by sino que. and our oranges here is one by sign of 8 -1 by concept. A scarred of Okay so while solving this problem we will come across a special condition. Okay without alleges will not be exactly equal to our marriage is okay in that situation what we have to do, we'll see in this problem. Okay this is a special case. It doesn't occur very often but if it does then this is the process we need to follow. Okay let's see one by Cossack minus court of minus one life sign. Ok so let's convert all of these in terms of silent costs. So this will be equal to one by sign a miner's because of a You know we have cause of any right Sign up here and then here we have one bite sign. Ok so first taking calcium over here we will have one bite 1- asked me by Sign A -1. Life. Scientific. This is equality sign here by one like this cost minus one by saying okay so taking L cm again here we will have sine squared a minus one minus cause a bye Sign into 1- because of it. Okay now converting sign square into one minus car squaring so minus here or then Yeah we have one minus parts of the right right Signed and until we have 1 -3. Yeah so now this is a square minus b square. This formula here this is a square minus B squared. So we'll write this as one minus cost into one place cause of a. Okay and you know we have minus one minus toss off the and then do I get right Some here 1- passed a So this is equal to taking common 1- costs outside. So here we will have one less cause of a -1 and until we have signed in and we have one minus boss 1- Cosine Cancell out. Okay and you have plus one and -1 cancels out. So here we have cause the right sign of this is equal to court. Now you can see this is not equal to our NHS isn't it? Look at this, this is something else. So what we'll do is that we hear we started to solve with our alleges in hand right now what we'll do is that we'll start to solve our RHS as well. Okay. No we'll start to swallow it just as well to see what comes. So here we have our our HSS one by signing a minus one by Kazakh airplane part of Okay so again changing this, I'll do this quickly. So here we will have one by sign of a plus. Here we have cause of a five sign up and then here we will have one by sign of a minus. We would have sign of a body one class cause of a taking calcium here what we'll have here one plus course of a Okay and then you will have minus sine square and then we will have to sign off into one place because of it. Okay so this will again week we'll do one plus or software and then you will have 1- costs square a the right right Signed eight times 1 less cost eight. So this is equal to one place cost a common and here we'll have one one minus cost. Alright so again here we will have sign off and then here we will have one place cost one plus cosine and plus cause it cancels out, plus one minus one cancels out. So here we will have minus minus plus that is equal to cause A and then you will have signed. This is equal to got it. Now, if you look at this carefully, our LHs is caught and our rhs here is also equal to caught. Okay this let's just is equal to our chest. Hence through. Okay, if you have any further doubts, please feel free to let me know. I'll be very happy to help. Thank you.

Okay, here we have the next one. We have sine inverse of negative on or trying to figure out the exact value of each of these pro sine inverse of one. And then tangent inverse of zero. We're gonna start with sign sign. We have negative one. So negative one. So sign of Fada is equal to negative one. If you think about thinks I incur, it starts off here. Goes up at Pi Over two. It goes to one That pie goes zero and at negative one, it's ATS re pi over two for coastline. Inverse of positive one call signs. Uh, curve starts at zero and it starts at one. Here goes toe zero at pi over to and it goes to negative one at pipe. So we have it here. Coastline inverse of one is pie, right? Not by like I said it. Zero right here. Contingent of zero is going to be zero. Ah, The reason being sign of zero is equal to zero. Coastline of zero is equal to one. So 0/1 is to go to zero. So that's why we get zero sine inverse of negative one. I'm gonna go back up here for a moment. We have three pi over two. But if you're on the interval of pi to pie, it can also be negative Pi over two as well. Those air both possibilities for it. If we go backwards, they could be It wouldn't be right here.

In this problem, but the stick Ruto's Antifa is equals two. Therefore we have E is equals two gotten worse off. Donald for minus Canon Rose off internal phone. This can be written us cotton verse of panel fucking brittleness. Courthouse five x 2 -9 minus canvas of Colonel faisal fight. Isis Francisco. Bye bye to minus alpha minus alpha, Which is equals two. Bye bye to minus welfare. We have alpha is equals two. Bye bye to minus of eight says to alpha while we are alpha is equals two. Bye bye for minus over to the baby house wrote off and he down just standing for us journals. Bye bye for minus A by two. Hence the correct option is not.


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