Hyperbolic Cosine of Sum/Corollary

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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

$\blacksquare$


Sources