Real Area Hyperbolic Sine of Reciprocal equals Real Area Hyperbolic Cosecant

Theorem
Everywhere that the function is defined:
 * $\sinh^{-1} \left({\dfrac 1 x}\right) = \operatorname{csch}^{-1} x$

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