Secant of i/Proof 1

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Theorem

$\sec i = \dfrac {2 e} {e^2 + 1}$


Proof

\(\ds \sec i\) \(=\) \(\ds \frac 1 {\cos i}\) Definition of Complex Secant Function
\(\ds \) \(=\) \(\ds \frac 1 {\frac e 2 + \frac 1 {2 e} }\) Cosine of $i$
\(\ds \) \(=\) \(\ds \frac {2 e} {e^2 + 1}\) multiplying denominator and numerator by $2 e$

$\blacksquare$