Relationship between sech, inverse Gudermannian, and cos

From specialfunctionswiki
Jump to: navigation, search

Theorem

The following formula holds: $$\mathrm{sech}(\mathrm{gd}^{-1}(x))=\cos(x),$$ where $\mathrm{sech}$ is the hyperbolic secant, $\mathrm{gd}^{-1}$ is the inverse Gudermannian, and $\cos$ is the cosine.

Proof

References