Sine of Sum

Theorem

 * $\sin \left({a + b}\right) = \sin a \cos b + \cos a \sin b$

where $\sin$ is the sine and $\cos$ is the cosine.

Geometric Proof

 * See Cosine of Sum/Geometric Proof.
 * Then apply the below Proof from Cosine of Sum.

Historical Note
These formulas were proved by François Viète in about 1579.

Also see

 * Cosine of Sum
 * Tangent of Sum