Double Angle Formulas/Hyperbolic Tangent/Proof 2

Theorem

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


Proof

\(\ds \tanh 2 x\) \(=\) \(\ds \tanh \left({x + x}\right)\)
\(\ds \) \(=\) \(\ds \frac {\tanh x + \tanh x} {1 + \tanh x \tanh x}\) Hyperbolic Tangent of Sum
\(\ds \) \(=\) \(\ds \frac {2 \tanh x} {1 + \tanh^2 x}\)

$\blacksquare$

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