Double Angle Formula for Hyperbolic Cosine/Corollary 2

Corollary to Double Angle Formula for Hyperbolic Cosine

$\cosh 2 x = 1 + 2 \sinh^2 x$

where $\cosh$ and $\sinh$ denote hyperbolic cosine and hyperbolic sine respectively.

Proof

\(\ds \cosh 2 x\)

\(=\)

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

Double Angle Formula for Hyperbolic Cosine

\(\ds \)

\(=\)

\(\ds \paren {1 + \sinh^2 x} + \sinh^2 \theta\)

Difference of Squares of Hyperbolic Cosine and Sine

\(\ds \)

\(=\)

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

$\blacksquare$

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 8$: Hyperbolic Functions: $8.25$: Double Angle Formulas