 Hi and welcome to the session, I am Deepika here. Let's discuss the question, show that the function given by fx is equal to sinx is part a, strictly increasing in open interval 0 to pi by 2, part b, strictly decreasing in open interval pi by 2 to pi, part c, neither increasing nor decreasing in open interval 0 to pi. So let's start the solution. Let us first understand the definition of increasing and decreasing function. Let f be continuous on close interval a, b and differentiable on open interval a, b. Then f is strictly increasing in open interval a, b if f dash x is greater than 0 for each x belongs to the open interval a, b. And f is strictly decreasing in an open interval a, b if f dash x is less than 0 for each x belongs to an open interval a, b. That is, 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 this is the key idea behind our question. We will use this key idea to solve the question. So let's start the solution. Our given function fx is equal to sinx, therefore f dash x is equal to cos x. Now, part a, since for each x belongs to an open interval 0 to pi by 2, cos x is greater than 0 because cosine function is positive in first and fourth quadrant. This implies f dash x is greater than 0, hence according to our key idea f is strictly increasing in open interval 0 to pi by 2. Now, part b, since for each x belongs to, each x belongs to pi by 2 to pi cos x is less than 0 because cosine function is negative in second quadrant. This implies f dash x is less than 0, this implies f is strictly decreasing in an open interval pi by 2 to pi. So let's move to the part c. Now from part a, increasing an open interval 0 to pi by 2 and from part b, increasing in an open interval pi by 2 to pi. Now the interval 0 to pi can be broken as 0 to pi by 2 and pi by 2 to pi. Hence, on an entire interval 0 to pi, f is neither increasing nor decreasing in 0 to pi, hence proved. I hope the question is clear to you. Why don't take care.