Cosecant of i/Proof 2

Theorem

$\csc i = \paren {\dfrac {2 e} {1 - e^2} } i$

Proof

\(\ds \csc i\)

\(=\)

\(\ds -i \csch 1\)

Hyperbolic Cosecant in terms of Cosecant

\(\ds \)

\(=\)

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

Definition of Hyperbolic Cosecant

\(\ds \)

\(=\)

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

multiplying denominator and numerator by $e$

\(\ds \)

\(=\)

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

$\blacksquare$