 Hello and welcome to this session. Let us understand the following problem today. Prove that 2 sin inverse 3 by 5 is equal to tan inverse 24 by 7. Now let us write the solution. Let sin inverse 3 by 5 is equal to theta which implies sin theta is equal to 3 by 5 which implies tan theta is equal to 3 by 4. Therefore theta is equal to tan inverse of 3 by 4. Therefore sin inverse of 3 by 5 is equal to tan inverse of 3 by 4 which is equal to theta. Therefore 2 sin inverse 3 by 5 is equal to 2 tan inverse 3 by 4 which is equal to tan inverse 2 into 3 by 4 by 1 minus 3 by 4 the whole square. This is by using the identity 2 tan inverse x is equal to tan inverse of 2 x by 1 minus x square if minus 1 is less than x is less than 1. Now this is equal to tan inverse of 24 by 7 which is equal to RHS. Hence 2 sin inverse of 3 by 2 is equal to tan inverse of 24 by 7 proved. I hope you understood the problem. Bye and have a nice day.