Double Angle Formulas/Hyperbolic Sine/Proof 1

Theorem

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


Proof

\(\ds \sinh 2 x\) \(=\) \(\ds \map \sinh {x + x}\)
\(\ds \) \(=\) \(\ds \sinh x \cosh x + \cosh x \sinh x\) Hyperbolic Sine of Sum
\(\ds \) \(=\) \(\ds 2 \sinh x \cosh x\)

$\blacksquare$

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