 Hello and welcome to the session. I am Deepika here. Let's discuss a question. Prove that the function f given by fx is equal to log sin x is strictly increasing on an open interval 0 to pi by 2 and strictly decreasing on an open interval pi by 2 to pi. So, let's start the solution. We know that a function is strictly increasing on an open interval where its derivative is positive and a function is strictly decreasing on an open interval where its derivative is negative. So, we have fx is equal to log sin x therefore f dash x is equal to 1 over sin x into cos x and this is equal to cot x. Now for less than pi by 2 cot x is positive therefore f dash x is positive for 2 less than x less than pi cot x is negative therefore f dash x is negative hence decreasing an open interval 0 to pi by 2 and strictly decreasing on an open interval pi by 2 to pi hence proved. I hope the solution is clear to you. Bye and check you.