 Hello and welcome to the session. Let us understand the following question today. Prove the following. 3 sin inverse x is equal to sin inverse of 3x minus 4x cube where x belongs to closed interval minus 1 by 2 comma 1 by 2. Now before starting the solution, let us write the identity which we will be using in the question which says sin 3 theta is equal to 3 sin theta minus 4 sin cube theta. This is the key idea towards our question. Now let us proceed with the solution. We suppose that sin inverse x is equal to theta which implies x is equal to sin theta. Now using the identity written in the key idea it implies sin theta is equal to 3x minus 4x cube substituting sin theta for x. So therefore 3 theta is equal to sin inverse of 3x minus 4x cube theta is equal to sin inverse x. So it can be written as 3 sin inverse x is equal to sin inverse of 3x minus 4x cube and this is our required result. Hence proved. I hope you have answered the question. Bye and have a nice day.