Cosine Function is Even/Proof 1

Proof
Recall the definition of the cosine function:


 * $\displaystyle \cos z = \sum_{n \mathop = 0}^\infty \left({-1}\right)^n \frac {z^{2 n} } {\left({2 n}\right)!} = 1 - \frac {z^2} {2!} + \frac {z^4} {4!} - \cdots$

From Even Power is Non-Negative:
 * $\forall n \in \N: z^{2 n} = \paren {-z}^{2 n}$

The result follows.