Difference between revisions of "Relationship between secant, Gudermannian, and cosh"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\sec(\mathrm{gd}(x))=\cosh(x),$$ | $$\sec(\mathrm{gd}(x))=\cosh(x),$$ | ||
where $\sec$ denotes the [[secant]], $\mathrm{gd}$ denotes the [[Gudermannian]], and $\cosh$ denotes the [[cosh|hyperbolic cosine]]. | where $\sec$ denotes the [[secant]], $\mathrm{gd}$ denotes the [[Gudermannian]], and $\cosh$ denotes the [[cosh|hyperbolic cosine]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:46, 8 June 2016
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.
