int_(0)^( pi/2)log(tan theta+cot theta)d theta=pi log2

Prove that int_(0)^( pi/2)log(tan theta+cot theta)backslash d theta=pi log2

int_(0)^((pi)/(2))(sec theta-tan theta)d theta

STATEMENT 1: int_(0)^((pi)/(4))log(1+tan theta)d theta=(pi)/(8)log2 STATEMENT 2:int_(0)^((pi)/(2))log sin theta d theta=-pi log2

If int_(0)^(pi//2) sin theta log sin theta d theta = log K then K is equal to (e=2.71)

Evaluate: int_(-pi)^(3 pi)log(sec theta-tan theta)d theta

STATEMENT 1: int_0^(pi/4)log(1+t a ntheta)d theta=pi/8log2. STATEMENT 2: int_0^(pi/2)logsin theta d theta =-pilog2.

Evaluate : int_(0)^((pi)/(4)) log(1+tan theta ) d theta

For theta in(0,(pi)/(2)), provethat int_(0)^( theta)log(1+tan theta tan x)dx=theta log(sec theta)

The value of the integral int_(-pi//4)^(pi//4)log(sec theta-tan theta)d theta is