Relationship between secant, Gudermannian, and cosh

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Theorem

The following formula holds: $$\sec(\mathrm{gd}(x))=\cosh(x),$$ where $\sec$ denotes the secant, $\mathrm{gd}$ denotes the Gudermannian, and $\cosh$ denotes the hyperbolic cosine.

Proof

References