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cos 2\pi / n + cos 4\pi / n + cos 6\pi/ n +...+ \cos 2n \pi/n =0

Source: Polish MO Finals 1958 p3

August 29, 2024
trigonometry

Problem Statement

Prove that if n n is a natural number greater than 1 1 , then
cos⁡2πn+cos⁡4πn+cos⁡6πn+…+cos⁡2nπn=0. \cos \frac{2\pi}{n} + \cos \frac{4\pi}{n} + \cos \frac{6\pi}{n} + \ldots + \cos \frac{2n \pi}{n} = 0.
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