Quadruple Angle Formulas/Hyperbolic Tangent

Theorem

 * $\tanh \left({4 x}\right) = \dfrac {4 \tanh x + 4 \tanh^3 x} {1 + 6 \tanh^2 x + \tanh^4 x}$

where $\tanh$ denotes hyperbolic tangent.

Also see

 * Quadruple Angle Formula for Hyperbolic Sine
 * Quadruple Angle Formula for Hyperbolic Cosine