Double Angle Formulas/Hyperbolic Sine/Proof 3
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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 |
$\blacksquare$