 Hello and welcome to the session. Let us understand the following problem. Prove that cos inverse 4 by 5 plus cos inverse 12 by 13 is equal to cos inverse 33 by 65, like the formula that we will be using in the problem. Cos inverse x plus cos inverse y is equal to cos inverse xy minus under root 1 minus x square under root 1 minus y square minus 1 is less than x, y is less than equal to 1 and plus y is greater than equal to 0. And cos inverse of xy minus under root 1 minus x square into under root 1 minus y square if minus 1 is less than equal to x, y is less than equal to 1 and x plus y is less than equal to 0. This is our key idea to the problem. Now let us write the solution. We will be using the formula cos inverse x plus cos inverse y is equal to cos inverse of xy minus under root 1 minus x square into 1 minus y square since minus 1 is less than x, y is less than equal to 1 and x plus y is greater than equal to 0. Where let us take x is equal to 4.5 and y is equal to 12 by 13. Therefore cos inverse of 4 by 5 plus cos inverse of 12 by 13 is equal to cos inverse of 4 by 5 into 12 by 13 minus under root 1 minus 4 by 5 the whole square into under root 1 minus 12 by 13 the whole square which is equal to cos inverse 48 by 65 minus 3 by 5 into 5 by which is equal to cos inverse of 48 by 65 minus 15 by 65 which is equal to cos inverse of 33 by 65 which is equal to RHS inverse of 4 by 5 plus cos inverse of 12 by 13 is equal to cos inverse of 33 by 65.