Derivative of Cosine Function/Proof 1

Proof
From the definition of the cosine function, we have:
 * $\ds \cos x = \sum_{n \mathop = 0}^\infty \paren {-1}^n \frac {x^{2 n} } {\paren {2 n}!}$

Then:

The result follows from the definition of the sine function.