1. Sep 4, 2014

### Dinheiro

1. The problem statement, all variables and given/known data
Calculate
$cos\frac{2\pi}{2n+1} + cos\frac{4\pi}{2n+1} + cos\frac{6\pi}{2n+1} + ... + cos\frac{2n\pi}{2n+1}$

2. Relevant equations
Complex equations, maybe :p

3. The attempt at a solution
Let's say
$z^{2n+1} = 1$
The sum is equivalent to the sum of the real even roots of the equation above. That's it. Ideas?

2. Sep 4, 2014

3. Sep 7, 2014

### Dinheiro

Those were basically my ideas, I just didn't write down my complete attempt at the solution, sorry. But I could find out what was missing in my resolution xD Thanks, Ray

4. Sep 7, 2014

### vela

Staff Emeritus
How are we supposed to see what's missing if you don't show us what you did?

5. Sep 8, 2014

### HallsofIvy

You mention that, in the complex plane, the given arguments lie equally spaced about the unit circle so did you consider using $cos(z)=(e^{iz}+ e^{-iz})/2$?

6. Sep 8, 2014

### Dinheiro

Actually, I didn't solve it this way, but nice one though! Thanks, hallsoflvy