Even Impulse Pair is Fourier Transform of Cosine Function

Theorem
Consider the (real) cosine function $\cos: \R \to \R$.

Then:
 * $\map \FF {\cos} = \operatorname {II}$

where:
 * $\FF$ denotes the Fourier transform
 * $\operatorname {II}$ denotes the even impulse pair function.