Power Reduction Formulas/Hyperbolic Cosine Cubed/Proof 3
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Theorem
- $\cosh^3 x = \dfrac {\cosh 3 x + 3 \cosh x} 4$
Proof
| \(\ds \cosh^3 x\) | \(=\) | \(\ds \cos^3 i x\) | Hyperbolic Cosine in terms of Cosine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {\map \cos {3 i x} + 3 \cos i x} 4\) | Cube of Cosine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {\cosh 3 x + 3 \cosh x} 4\) | Hyperbolic Cosine in terms of Cosine |
$\blacksquare$