# Hyperbolic Cosine of Sum/Corollary

## Corollary of Hyperbolic Cosine of Sum

$\map \cosh {a - b} = \cosh a \cosh b - \sinh a \sinh b$

where $\sinh$ denotes the hyperbolic sine and $\cosh$ denotes the hyperbolic cosine.

## Proof

 $\displaystyle \map \cosh {a - b}$ $=$ $\displaystyle \cosh a \, \map \cosh {-b} + \sinh a \, \map \sinh {-b}$ Hyperbolic Sine of Sum $\displaystyle$ $=$ $\displaystyle \cosh a \cosh b - \sinh a \sinh b$ Hyperbolic Cosine Function is Even and Hyperbolic Sine Function is Odd

$\blacksquare$