Difference between revisions of "Relationship between cosine, Gudermannian, and sech"
From specialfunctionswiki
| Line 1: | Line 1: | ||
<div class="toccolours mw-collapsible mw-collapsed"> | <div class="toccolours mw-collapsible mw-collapsed"> | ||
| − | <strong>Theorem:</strong> The following formula holds: | + | <strong>[[Relationship between cosine, Gudermannian, and sech|Theorem]]:</strong> The following formula holds: |
$$\cos(\mathrm{gd}(x))=\mathrm{sech}(x),$$ | $$\cos(\mathrm{gd}(x))=\mathrm{sech}(x),$$ | ||
where $\cos$ denotes the [[cosine]], $\mathrm{gd}$ denotes the [[Gudermannian]], and $\mathrm{sech}$ denotes the [[sech|hyperbolic secant]]. | where $\cos$ denotes the [[cosine]], $\mathrm{gd}$ denotes the [[Gudermannian]], and $\mathrm{sech}$ denotes the [[sech|hyperbolic secant]]. | ||
Revision as of 22:51, 25 August 2015
Theorem: The following formula holds: $$\cos(\mathrm{gd}(x))=\mathrm{sech}(x),$$ where $\cos$ denotes the cosine, $\mathrm{gd}$ denotes the Gudermannian, and $\mathrm{sech}$ denotes the hyperbolic secant.
Proof: █
