Sine of i/Proof 2

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

\(\ds \)

\(=\)

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

$\blacksquare$