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

\(\ds \)

\(=\)

\(\ds 2 \sinh x \cosh x\)

$\blacksquare$