Cosine Function is Even/Proof 1

Proof
Recall the definition of the cosine function:


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

From Even Powers are Positive, we have that:
 * $\forall n \in \N: x^{2 n} = \left({-x}\right)^{2 n}$

The result follows.