I=int_(0)^( pi/2)sin2kx*cot xdx

If for k in N backslash(sin2kx)/(sin x)=2[cos x+cos3x+...+cos(2k-1)x] Then the value of I=int_(0)^( pi/2)sin2kx*cot x backslash dx is

int_(0)^( pi/2)sin^2xcos xdx

int_(0)^( pi/2)sin xdx

int_(0)^( pi/2)sin xdx

int_(0)^( pi/2)sin xdx

int_(0)^( pi/2)sin^(2)x cos xdx

int_(0)^( pi/2)sin xdx=

The value of the integral int_(0)^((pi)/(2))sin2nx cot xdx where n is positive,is

Prove that for any positive integer k,(sin2kx)/(sin x)=2[cos x+cos3x+...+cos(2k-1)x] Hence,prove that int_(0)^((pi)/(2))sin2xk cot xdx=(pi)/(2)

Find the value of int_(0)^(pi//2)sin2xlogtan xdx .