Sine of i/Proof 1

Theorem

 * $\displaystyle \sin i = \left({ \frac e 2 - \frac 1 {2e} }\right) i$

where $\sin$ denotes the complex sine function and $i$ is the imaginary unit.

Proof
We have:

Also:

Therefore:

Then from $\left({1}\right) - \left({2}\right)$: