Given (sin2kx)/(sin x)=2[cos x+cos 3x+…+...

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)`.

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