Prosthaphaeresis Formulas/Hyperbolic Cosine minus Hyperbolic Cosine

Theorem

 * $\cosh x - \cosh y = 2 \, \map \sinh {\dfrac {x + y} 2} \, \map \sinh {\dfrac {x - y} 2}$

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