Difference between revisions of "Relationship between cosine, Gudermannian, and sech"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | 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]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:42, 8 June 2016
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.
