Hyperbolic Tangent Half-Angle Substitution for Cosine

Corollary to Double Angle Formula for Hyperbolic Cosine

 * $\cosh 2 x = \dfrac {1 + \tanh^2 x}{1 - \tanh^2 x}$

where $\cosh$ and $\tanh$ denote hyperbolic cosine and hyperbolic tangent respectively.