Laplace Transform of Cosine/Proof 3

Theorem
Let $\cos$ be the real cosine function.

Let $\mathcal L$ be the Laplace Transform.

Then:


 * $\displaystyle \mathcal L \left\{{\cos at}\right\} = \frac s {s^2+a^2}$

where $a \in \R$ is constant, and $\operatorname{Re}\left({s}\right) > a$.