 Hello and welcome to the session. In this session we discussed the following question which says show that 2 into cos inverse y is equal to cos inverse of 2y square minus 1. Before we move on to the solution let's recall one identity which says that cos 2 theta is equal to 2 cos square theta minus 1. This is the key idea that we use for this question. Now we move on to the solution. We have to show that 2 cos inverse y is equal to cos inverse of 2y square minus 1. First of all we take let y be equal to cos theta. Now let's consider the RHS first. We have the RHS is equal to cos inverse of 2y square minus 1. Now putting the value for y as cos theta we get this is equal to cos inverse of 2 cos square theta minus 1. Now from the key idea as you can see we have an identity that is cos 2 theta is equal to 2 cos square theta minus 1. And so this is equal to cos inverse of cos 2 theta as 2 cos square theta minus 1 is cos 2 theta. And cos inverse of cos 2 theta would be equal to 2 theta. Now when we take y is equal to cos theta this would mean that theta is equal to cos inverse y. So putting the value for this theta here that is in 2 theta we get this would be equal to 2 into cos inverse y. Which is the same as the LHS as we get the RHS is equal to the LHS and we were supposed to prove this. So hence proved this completes the session. Hope you have understood the solution of this question.