Power Reduction Formulas/Hyperbolic Sine Squared/Proof 1

Theorem

$\sinh^2 x = \dfrac {\cosh 2 x - 1} 2$

Proof

\(\ds 2 \sinh^2 x + 1\)

\(=\)

\(\ds \cosh 2 x\)

Double Angle Formula for Hyperbolic Cosine: Corollary $2$

\(\ds \leadsto \ \ \)

\(\ds \sinh^2 x\)

\(=\)

\(\ds \frac {\cosh 2 x - 1} 2\)

solving for $\sinh^2 x$

$\blacksquare$