Double Angle Formulas/Hyperbolic Sine/Proof 3

Theorem

$\sinh 2 x = 2 \sinh x \cosh x$


Proof

\(\ds \sinh 2 x\) \(=\) \(\ds -i \sin 2 i x\) Hyperbolic Sine in terms of Sine
\(\ds \) \(=\) \(\ds -2 i \sin i x \cos i x\) Double Angle Formula for Sine
\(\ds \) \(=\) \(\ds 2 \sinh x \cosh x\) Hyperbolic Sine in terms of Sine, Hyperbolic Cosine in terms of Cosine

$\blacksquare$

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