# Cosine of Sum/Corollary

(Redirected from Cosine of Difference)

## Corollary to Cosine of Sum

$\map \cos {a - b} = \cos a \cos b + \sin a \sin b$

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

## Proof

 $\displaystyle \map \cos {a - b}$ $=$ $\displaystyle \cos a \, \map \cos {-b} - \sin a \, \map \sin {-b}$ Cosine of Sum $\displaystyle$ $=$ $\displaystyle \cos a \cos b - \sin a \, \map \sin {-b}$ Cosine Function is Even $\displaystyle$ $=$ $\displaystyle \cos a \cos b + \sin a \sin b$ Sine Function is Odd

$\blacksquare$

## Historical Note

The Cosine of Sum formula and its corollary were proved by François Viète in about $1579$.