 Hello and welcome to the session. In this session we discussed the following question that says, prove the following tan inverse square root x is equal to 1 upon 2 cos inverse of 1 minus x upon 1 plus x where x belongs to the open interval 0, 1. Before we move on to the solution, let's discuss one formula which is cos 2x is equal to 1 minus tan square x upon 1 plus, this is the key idea that we use in this question. Let's proceed with the solution now. We have to prove the inverse of square root x is equal to 1 upon 2 cos inverse of 1 plus x and this x belongs to the open interval 0, 1. For this we suppose is equal to, this is equal to tan y, so this means that we get this is equal to 1 upon plus inverse of 1 minus, key idea we get that cos 2x is equal to 1 minus tan square x upon 1 plus tan square x, 1 minus tan square y upon 1 plus tan square y, we can put of 2y, so this is equal to 1 upon 2 cos inverse of 2 into 2y, x is equal to x is with 2 and this is equal to y and we know that y is tan inverse square root x, square root x which is the LHS equal to DLHS, we open interval 0, 1. In this session we will understand the solution of this question.