Prosthaphaeresis Formulas/Hyperbolic Cosine minus Hyperbolic Cosine

Theorem

 * $\cosh x - \cosh y = 2 \sinh \left({\dfrac {x + y} 2}\right) \sinh \left({\dfrac {x - y} 2}\right)$

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