 Hello and welcome to the session. In this session we discussed the following question which says, prove that 1 plus cot a minus cosec a into 1 plus tan a plus sec a equal to 2. Let's move on to the solution. We have to prove that 1 plus cot a minus cosec a into 1 plus tan a plus sec a equal to 2. So let's consider the LHS that is 1 plus cot a minus cosec a into 1 plus tan a plus sec a. Now this could be written as 1 plus cos a upon sin a since we know that cot a is equal to cos a upon sin a minus 1 upon sin a since cosec a is equal to 1 upon sin a into 1 plus. Now tan a is sin a upon cos a plus sec a which is 1 upon cos a. And this is equal to by taking Lcm we get sin a in denominator and in the numerator we get sin a plus cos a minus 1 whole into by taking Lcm we get cos a in the denominator and in the numerator we get cos a plus sin a plus 1. So multiplying both these brackets we get sin a into cos a in the denominator and in the numerator we have sin a plus cos a minus 1 into sin a plus cos a plus 1. We know that x minus y into x plus y is equal to x square minus y square. So this would be equal to sin a plus cos a the whole square minus 1 the whole square upon sin a into cos a. Now we know the identity a plus v the whole square equal to a square plus 2 a b plus b square. So we apply this identity in this first bracket. So this would be equal to sin square a plus cos square a plus 2 sin a into cos a minus 1 square that is 1 whole upon sin a into cos a. We know that sin square a plus cos square a is equal to 1. So this would be equal to 1 plus 2 sin a into cos a minus 1 upon sin a into cos a. So this 1 and this minus 1 gets cancelled and we are left with 2 sin a into cos a upon sin a into cos a. Now sin a sin a cancels cos a cos a cancels. So we are left with 2 which is equal to the RHS. So we get the LHS is equal to the RHS. So hence proved. This completes the session. Hope you have understood the solution of this question.