 Hello and welcome to the session. The given question says, if set theta plus tan theta is equal to p, prove that sin theta is equal to p square minus 1 divided by p square plus 1. Let's move on to the solution. Now we have to prove that sin theta is equal to p square minus 1 divided by p square plus 1. And this is the right hand side. Now we shall start with the right hand side to show that it is equal to the left hand side of what we have to prove, which is sin theta. So right hand side is p square minus 1 divided by p square plus 1. On substituting the value of p we have, set theta plus tan theta whole square minus 1 divided by set theta plus tan theta whole square plus 1. Now this is further equal to set square theta plus tan square theta plus 2 times of set theta into tan theta minus 1 whole divided by set square theta plus tan square theta plus 2 times of set theta into tan theta plus 1. And thus we have written by using the identity that a plus b whole square is equal to a square plus b square plus 2 times of a into b. Now we know that 1 plus tan square theta is equal to set square theta. So by using this this can further be written as, now set square theta minus 1 is equal to tan square theta. There is one more tan square theta so we have 2 times of tan square theta plus 2 set theta into tan theta whole divided by, now here tan square theta plus 1 is equal to set square theta and 1 set square theta is already in the denominator. So again we have 2 times of set square theta plus 2 times of set theta into tan theta. Now let us take the common terms from the numerator and denominator outside. So we have 2 times of tan theta which is common in both the terms on the numerator. So we are left with tan theta plus set theta. Now take it 2 set theta common from the denominator we have set theta plus tan theta. Now cancelling the common terms from the numerator and denominator we have tan theta divided by set theta. Now tan theta is sin theta divided by cos theta. Set theta is 1 divided by cos theta. So this is further equal to sin theta divided by cos theta into cos theta divided by 1. Again on cancelling cos theta from the numerator and denominator we have sin theta and this is the right hand side. Therefore we have that sin theta is equally equal to p square minus 1 divided by p square plus 1. So this proves hope you have understood it well. Bye and take care.