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

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

By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(sin x-cos x)/(1+sin x cos x)dx

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a-x) dx . Hence, evaluate int_(0)^(pi//2) (sin x - cos x)/(1+ sin x cos x) dx.

Prove that : int_(0)^(pi//2) (sin x-cos x)/(1+sin x cos x)dx=0 " (ii) Prove that " : int_(0)^(pi//2) sin 2x. log (tan-x) dx=0

Prove that : int_(0)^(pi//2) (sin x-cos x)/(1+sin x cos x)dx=0 " (ii) Prove that " : int_(0)^(pi//2) sin 2x. log (tan-x) dx=0

I_(1)=int_(0)^((pi)/(2))(sin x-cos x)/(1+sin x cos x)dx,I_(2)=int_(0)^(2 pi)cos^(6)xdx,I_(3)=int_((pi)/(2))^((pi)/(2))sin^(3)xdx,I_(4)=int_(0)^(1)1n((1)/(x)-1)dx. Then I_(1)=I_(3)=I_(4)=0,I_(1)!=0I_(1)=I_(3)=0,I_(4)!=0I_(1)=I_(2)=0,I_(4)!=0I_(1)=I_(2)=I_(3)=0,I_(4)!=0

Using properties of definite integrals, evaluate: int_(0)^(pi//2) (sin x - cos x)/(1+sin x cos x) dx

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

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