Real Area Hyperbolic Tangent of Reciprocal equals Real Area Hyperbolic Cotangent

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

where $\tanh^{-1}$ and $\coth^{-1}$ denote inverse hyperbolic tangent and inverse hyperbolic cotangent respectively.