Prosthaphaeresis Formulas/Hyperbolic Sine minus Hyperbolic Sine

Theorem

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

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