Mathematics

Problem

Let

I = \int_{0}^{\pi/2} \frac{\cos x}{a \cos x + b \sin x}\, dx

and

J = \int_{0}^{\pi/2} \frac{\sin x}{a \cos x + b \sin x}\, dx

, where

a > 0

and

b > 0

. Compute the values of

I

and

J