$\int_0^{\frac{\pi}{2}} \frac{\cos x-\sin x}{1+\cos x \sin x}$ is equal to

Question

Professor PC Thomas Classes · Answer

Use $I = \int_0^{\pi/2} f(x)dx = \int_0^{\pi/2} f(\pi/2-x)dx$. Adding them gives $2I = 0 \implies I = 0$.