 Hello and welcome to the session. In this session we are going to discuss the following question which says that if u is equal to cos inverse of square root of sin of alpha minus sin inverse of square root of sin of alpha then find the value of sin of pi by 4 minus u by 2 sin inverse of x plus cos inverse of x is equal to pi by 2 for all x belonging to the closed interval minus 1 to 1 with this key idea let us proceed with the solution using the key idea we know that sin inverse of x plus cos inverse of x is equal to pi by 2 that is sin inverse of x plus cos inverse of x is equal to pi by 2 as we can write cos inverse of x is equal to pi by 2 minus sin inverse of x we are given u is equal to cos inverse of square root of sin of alpha minus sin inverse of square root of sin of alpha so here we can replace cos inverse of square root of sin of alpha with pi by 2 minus sin inverse of square root of sin of alpha in the above equation therefore we get u is equal to pi by 2 minus sin inverse of square root of sin of alpha minus sin inverse of square root of sin of alpha and u is equal to pi by 2 minus sin inverse of square root of sin of alpha minus sin inverse of square root of sin of alpha which can be written as u is equal to pi by 2 minus 2 sin inverse of square root of sin of alpha all we can write to sin inverse of square root of sin of alpha is equal to pi by 2 minus u that is sin inverse of square root of sin of alpha is equal to pi by 4 minus u by 2 which can be written as square root of sin of alpha is equal to sin of pi by 4 minus u by 2 therefore we can write the value of sin of pi by 4 minus u by 2 is given by square root of sin of alpha which is the required answer this completes our session hope you enjoyed this session