# Sine of Sum/Corollary

## Corollary to Sine of Sum

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

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

## Proof

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

$\blacksquare$

## Historical Note

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