Cosine to Power of Odd Integer/Proof 1

Theorem

 * $\displaystyle \cos^{2n+1} \theta = \frac 1 {2^{2n}} \left({\cos \left({2n+1}\right) \theta + \binom{2n+1} 1 \cos \left({2n-1}\right) \theta + \cdots + \binom{2n+1} n \cos \theta}\right)$

That is:
 * $\displaystyle \cos^{2n+1} \theta = \frac 1 {2^{2n}} \sum_{k \mathop = 0}^n \binom {2n+1} k \cos \left({2n - 2k + 1}\right) \theta$