Real Area Hyperbolic Cosine of Reciprocal equals Real Area Hyperbolic Secant

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

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