# Proving Identity

1. Nov 7, 2007

### Dragonfall

1. The problem statement, all variables and given/known data
Show that $$\prod_{k=1}^{n-1}\sin\frac{k\pi}{2n}=\frac{\sqrt{n}}{2^{n-1}}$$

3. The attempt at a solution

I have no idea where to start.

2. Nov 7, 2007

### morphism

Let $\zeta$ be the primitive (2n)th root of unity, i.e. $\zeta = \exp(\pi i / n)$. Try to simplify $|1 - \zeta^k|$ (where k is some positive integer). Then try playing around with x^(2n) - 1.