Hyperbolic Secant Function is Even/Proof 1

Theorem

$\map \sech {-x} = \sech x$

Proof

\(\ds \map \sech {-x}\)

\(=\)

\(\ds \frac 1 {\map \cosh {-x} }\)

Definition 2 of Hyperbolic Secant

\(\ds \)

\(=\)

\(\ds \frac 1 {\cosh x}\)

Hyperbolic Cosine Function is Even

\(\ds \)

\(=\)

\(\ds \sech x\)

$\blacksquare$