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

Prove that: int_(0)^( pi/2)(sin x)/(sin x-cos x)dx=(pi)/(4)

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

(sin 2 kx)/(sin x)=2[cos x + cos 3 x + …+cos (2k -1)x] , then value of I=int_(0)^(pi//2)(sin 2 k x)/(sin x)cos x dx is :

(sin 2 kx)/(sin x)=2[cos x + cos 3 x + …+cos (2k -1)x] , then value of I=int_(0)^(pi//2)(sin 2 k x)/(sin x)cos x dx is :

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

int_(0)^((pi)/(2))(x)/(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:

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

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

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