Power Reduction Formulas/Hyperbolic Cosine Cubed/Proof 1
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Theorem
- $\cosh^3 x = \dfrac {\cosh 3 x + 3 \cosh x} 4$
Proof
| \(\ds \cosh 3 x\) | \(=\) | \(\ds 4 \cosh^3 x - 3 \cosh x\) | Triple Angle Formula for Hyperbolic Cosine | |||||||||||
| \(\ds \leadsto \ \ \) | \(\ds 4 \cosh^3 x\) | \(=\) | \(\ds \cosh 3 x + 3 \cosh x\) | rearranging | ||||||||||
| \(\ds \leadsto \ \ \) | \(\ds \cosh^3 x\) | \(=\) | \(\ds \dfrac {\cosh 3 x + 3 \cosh x} 4\) | dividing both sides by $4$ |
$\blacksquare$