Question

Tính C = \(cos\frac{\Pi}{9}+cos\frac{2\Pi}{9}+....+cos\frac{8\Pi}{9}+cos\Pi\)

A . 0

B . 1

C . 2

D . -1

Answer 1

\(C=cos\frac{\pi}{9}+cos\frac{8\pi}{9}+cos\frac{2\pi}{9}+cos\frac{7\pi}{9}+...+cos\frac{4\pi}{9}+cos\frac{5\pi}{9}+cos\pi\)

\(C=cos\frac{\pi}{9}+cos\left(\pi-\frac{\pi}{9}\right)+cos\frac{2\pi}{9}+cos\left(\pi-\frac{2\pi}{9}\right)+...+cos\frac{4\pi}{9}+cos\left(\pi-\frac{4\pi}{9}\right)-1\)

\(C=cos\frac{\pi}{9}-cos\frac{\pi}{9}+cos\frac{2\pi}{9}-cos\frac{2\pi}{9}+...+cos\frac{4\pi}{9}-cos\frac{4\pi}{9}-1\)

\(C=-1\)