Sine of Sum/Proof 4

Theorem

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

where $\sin$ is the sine.

Proof
Recall the Cosine of Sum:


 * $ \displaystyle \cos(a + b) = \cos a \cos b - \sin a \sin b $

Now, using the identity $\cos \left({\frac \pi 2 - a}\right) = \sin a$ from Sine equals Cosine of Complement, we have: