a question on trigonometry

Question

Can anyone tell me why $$1/2+\cos x+\cos 2x+\cdots+\cos nx=\frac{\sin((n+1/2)x)}{2\sin (x/2)}\text{ ?}$$

I think this question has appeared a few times before? – Michael Hardy Feb 16 '15 at 06:02 — Michael Hardy, Feb 16 '15 at 06:02

score 0 · Answer 1 · answered Feb 16 '15 at 06:01

0

Hint: $2\sin\left(\frac{x}{2}\right)\cdot \cos (nx)=\sin \left(\frac{(2n+1)x}{2}\right)-\sin\left(\frac{(2n-1)x}{2}\right)$

answered Feb 16 '15 at 06:01

DeepSea

score 0 · Answer 2 · edited Feb 16 '15 at 06:25

0

$2\sin(\frac{x}{2})*\cos(nx) = \sin((n+\frac{1}{2})x)-\sin((n-\frac{1}{2})x)$

it cancel each other out

edited Feb 16 '15 at 06:25

answered Feb 16 '15 at 06:03

mohlee

2 Answers2