Tangent of i/Proof 2
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Theorem
- $\tan i = \paren {\dfrac {e^2 - 1} {e^2 + 1} } i$
Proof
| \(\ds \tan i\) | \(=\) | \(\ds i \tanh 1\) | Hyperbolic Tangent in terms of Tangent | |||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {\frac {e^1 - e^{-1} } {e^1 + e^{-1} } } i\) | Definition of Hyperbolic Tangent | |||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {\frac {e^2 - 1} {e^2 + 1} } i\) | multiplying denominator and numerator by $e$ |
$\blacksquare$