Cosine of Sum

Theorem

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


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

where $\sin$ and $\cos$ are sine and cosine.

Corollary

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


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

Proof of Corollary
Similarly, we obtain:

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