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 $e$
\(\ds \) \(=\) \(\ds \paren {\frac {1 + e^2} {1 - e^2} } i\)

$\blacksquare$