Hyperbolic Sine Function is Odd/Proof 2
Jump to navigation
Jump to search
Theorem
- $\map \sinh {-x} = -\sinh x$
Proof
| \(\ds \map \sinh {-x}\) | \(=\) | \(\ds -i \, \map \sin {-i x}\) | Hyperbolic Sine in terms of Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds i \, \map \sin {i x}\) | Sine Function is Odd | |||||||||||
| \(\ds \) | \(=\) | \(\ds -\sinh x\) | Hyperbolic Sine in terms of Sine |
$\blacksquare$