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