Cosecant of i/Proof 1
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Theorem
- $\csc i = \paren {\dfrac {2 e} {1 - e^2} } i$
Proof
| \(\ds \csc i\) | \(=\) | \(\ds \frac 1 {\sin i}\) | Definition of Complex Cosecant Function | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac 1 {\paren {\frac e 2 - \frac 1 {2 e} } i}\) | Sine of $i$ | |||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {\frac 1 {\frac 1 {2 e} - \frac e 2} } i\) | Reciprocal of $i$ | |||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {\frac {2 e} {1 - e^2} } i\) | multiplying denominator and numerator by $2 e$ |
$\blacksquare$