 Hello and welcome to the session. Let us understand the following problem. Fuse that cos inverse 12 by 13 plus sin inverse 3 by 5 is equal to sin inverse 56 by 65. Now we will be using the following identity. Sin of alpha plus beta is equal to sin alpha cos beta plus cos alpha sin beta. This is our key idea. Now let us write the solution. Consider left inside let cos inverse 12 by 13 is equal to A. Let us name this as 1, which implies cos A is equal to 12 by 13. And then by using Pythagoras theorem we get sin A is equal to 5 by 13 by Pythagoras theorem. Now let sin inverse 3 by 5 is equal to B. Let us name it as 2. Therefore it implies sin B is equal to 3 by 5. Again by using Pythagoras theorem we get cos B is equal to 4 by 5. Now using this identity that we wrote in key idea that is sin of A plus B is equal to sin A cos B plus cos A sin B. Now substituting the values we get which is equal to 5 by 13 into 4 by 5 plus 12 by 13 into 5 by 3 by 5 which is equal to 56 by 65. Therefore A plus B is equal to sin inverse of 56 by 65 which implies cos inverse of 12 by 13 plus sin inverse of 3 by 5 is equal to sin inverse of 56 by 65. This is by using 1 and 2. Now we have got the desired result so hence proved. I hope you understood this problem. Bye and have a nice day.