Cosine of Half-Integer Multiple of Pi

Theorem
Let $x \in \R$ be a real number.

Let $\cos x$ denote the cosine of $x$.

Then:
 * $\forall n \in \Z: \cos \left({n + \dfrac 1 2}\right) \pi = 0$

Proof
This is established in Zeroes of Sine and Cosine.