The trigonometric summation formulae

This little demo walks through the proof of the trig summation formulae: $$ \begin{aligned} \sin(\alpha+\beta) &= \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta), \text{ and} \\ \cos(\alpha+\beta) &= \cos(\alpha)\cos(\beta) - \sin(\alpha)\sin(\beta). \end{aligned} $$