Double Angle Formula for Hyperbolic Cosine/Corollary 1
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Corollary to Double Angle Formula for Hyperbolic Cosine
- $\cosh 2 x = 2 \cosh^2 x - 1$
where $\cosh$ denotes hyperbolic cosine.
Proof
| \(\ds \cosh 2 x\) | \(=\) | \(\ds \cosh^2 x + \sinh^2 x\) | Double Angle Formula for Hyperbolic Cosine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \cosh^2 x + \paren {\cosh^2 x - 1}\) | Difference of Squares of Hyperbolic Cosine and Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds 2 \cosh^2 x - 1\) |
$\blacksquare$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 8$: Hyperbolic Functions: $8.25$: Double Angle Formulas