Power Reduction Formulas/Hyperbolic Cosine Squared/Proof 1
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Theorem
- $\cosh^2 x = \dfrac {\cosh 2 x + 1} 2$
Proof
| \(\ds 2 \cosh^2 x - 1\) | \(=\) | \(\ds \cosh 2 x\) | Double Angle Formula for Hyperbolic Cosine: Corollary $1$ | |||||||||||
| \(\ds \cosh^2 x\) | \(=\) | \(\ds \frac {\cosh 2 x + 1} 2\) | solving for $\cosh^2 x$ |
$\blacksquare$