 Hello and welcome to this session. Let us understand the following problem today. Write the following function in the simplest form. We have time inverse of an order 1-cos x by 1 plus cos x where x is less than pi. Now in this question we will be using the following identities. 1 plus cos x is equal to 2 cos square x by 2 and 1 minus cos x is equal to 2 sin square x by 2. Let us name them as 1 and 2. Now let us write the solution. We have tan inverse of under root 1 minus cos x by 1 plus cos x is equal to tan inverse of under root 2 sin square x by 2 divided by 2 cos square x by 2. This is by using 1 and 2. Now this 2 gets cancelled. So we are left with which is equal to tan inverse of sin x by 2 by cos x by 2 which is equal to tan inverse of tan x by 2 which is equal to x by 2 where x is less than pi. Hence the required answer is x by 2. I hope you understood this session. Bye and have a nice day.