Real Area Hyperbolic Sine of Reciprocal equals Real Area Hyperbolic Cosecant

Theorem
Everywhere that the function is defined:
 * $\map {\sinh^{-1} } {\dfrac 1 x} = \csch^{-1} x$

where $\sinh^{-1}$ and $\csch^{-1}$ denote inverse hyperbolic sine and inverse hyperbolic cosecant respectively.