Prove that for any positive integer , 2Kx x = 2[ x + 3x + + (2K-1)x] Hence

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Prove that for any positive integer KK , sin⁡2Kxsin⁡x=2[cos⁡x+cos⁡3x+⋯+cos⁡(2K−1)x]\frac{\sin 2Kx}{\sin x} = 2[\cos x + \cos 3x + \dots + \cos(2K-1)x] Hence, prove that ∫0π/2sin⁡2Kx⋅cot⁡xdx=π2\int_0^{\pi/2} \sin 2Kx \cdot \cot x dx = \frac{\pi}{2} .

Related theory

Browse the problem library