Sine of i/Proof 2
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Theorem
- $\sin i = \paren {\dfrac e 2 - \dfrac 1 {2 e} } i$
Proof
\(\ds \sin i\) | \(=\) | \(\ds i \sinh 1\) | Hyperbolic Sine in terms of Sine | |||||||||||
\(\ds \) | \(=\) | \(\ds i \frac {e^1 - e^{-1} } 2\) | Definition of Hyperbolic Sine | |||||||||||
\(\ds \) | \(=\) | \(\ds \paren {\frac e 2 - \frac 1 {2 e} } i\) |
$\blacksquare$