00:00So, the question here is, if sin theta and cos theta are the roots of this equation,
00:05then which one of the following is correct?
00:07So, first of all, we all can see A is square, B is square, and two H terms in all
00:13four options.
00:14Which means there will be some relation to it.
00:16Now, we know that sum of roots which is roots are sin theta and cos theta,
00:24the sum of roots is sin theta plus cos theta is equal to minus B upon A.
00:29And the product of roots is, which is sin theta, cos theta is equal to C upon A.
00:37So, now if we need B upon A and C upon A in this equation, so what can we do?
00:44So, the thing which we can do here is, divide this equation by A square.
00:52So, if we divide A square, then this becomes 1, this term becomes 1, and this one becomes
01:01B upon A whole square, and B square upon A square, we can also write it B upon A whole
01:10square,
01:12and 2, C upon A, C upon A, A square, is square to A above cancel.
01:22So, now these are 3 terms, now we will determine the sign later on.
01:28So, first of all, B upon A is, B upon A is, minus B upon A is, sin theta plus
01:35cos theta.
01:36So, B upon A is, minus sin theta, minus sin theta, plus cos theta.
01:42But, if we square, then minus sin will remove, which means, this middle term is, sin theta plus cos theta
01:50is square,
01:51whole square, so it will become, sin square theta, plus cos square theta, plus 2 sin theta, cos theta.
02:03Now, we know, this will become 1, and this will become, 1 plus 2 sin theta, cos theta, 2 sin
02:13theta, cos theta,
02:15and here, 2 C upon A, sin theta, cos theta, so here it will come, 2 sin theta, cos theta.
02:23Now, we have to determine, which sign to put, here the equals is in 0, so we will have to
02:29bring 0.
02:30So, if we, put positive on it, and then, put these 2 in negative, and this 1 in positive,
02:39then this will cancel this, and this will cancel this, so, minus A square, plus B square, minus 2 C
02:48option will also be correct.
02:50But, since that is not in the options list, so in option number C, it is not A square, plus
02:58B square, plus 2 C option number C,
03:01is, is, we will write it downward, option number C, is, we will write it downward, option number C,
03:07is, A square, minus B square, plus 2 C, now we can see, 1 plus 2 sin theta, cos theta,
03:14minus 1, minus 2 sin theta, cos theta.
03:17So, option number C will be the final answer, option number C, it will be the final answer.
03:23And, if not questions mustga business, please do.
03:23Thank you.
