Sum of Cosines of k pi over 5

Theorem

 * $\cos 36 \degrees + \cos 72 \degrees + \cos 108 \degrees + \cos 144 \degrees = 0$

Proof
We have:

and:

Thus:
 * $\cos 36 \degrees + \cos 72 \degrees + \cos 108 \degrees + \cos 144 \degrees = 0$


 * Sum of Cosines of k pi over 5.png