Prove that for any positive integer `k ,(sin2k x)/(sinx)=2[cosx+cos3x++cos(2k-1)x]dot` Hence, prove that `int_0^(pi/2)sin2x kcotxdx=pi/2dot`

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)

Prove that for any positive integer K, (sin2kx)/(sinx)=2[cos x + cos 3x+....+ cos (2k-1)x] Hence , proved that int_(0)^(pi//2) sin 2kx. Cot x dx = (pi//2)

Prove that: int_0^(pi//2)(sin x)/(sinx-cosx)dx=pi/4

Given (sin2kx)/(sin x)=2[cos x+cos 3x+…+ cos(2k-1)x] , where k is a positive integer, show that, int_(0)^((pi)/(2))sin2 kx cotx dx=(pi)/(2) .

(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 :

Prove that int_0^(pi//4) cos^2 2x sin^3 4x dx=1/6

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

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

Prove that int_0^pi x/(a^2cos^2x+b^2sin^2x)dx=pi^2/(2ab)