int_(0)^( pi/2)(cos x)/((1+sin x)(2+sin x))dx

int_(0)^( pi/2)(sin x)/(1+cos x)dx

int_(0)^(pi//2) (Cos x)/(1+Sin x) dx=

int_(0)^(pi//2) ( cos x - sin x )/( 2 + sin x cos x ) dx is equal to

int_(0)^( pi/2)((sin x cos x) /(1+sin 4x ))dx

int_(0)^(pi//2) (sin x cos x) / ((1 + 2 sin x ) ( 1+ sin x))dx =

int_(0)^( pi/2)(sin x-cos x)/(1+sin x*cos x)*dx

If int_(0)^((pi)/(2))(dx)/(1+sin x+cos x)=In2, then the value of int_(0)^((pi)/(2))(sin x)/(1+sin x+cos x)dx is equal to:

Prove that int_(0)^(pi//2) (sin x -cos x)/(1+sin x cos x)dx = 0 .