Difference between revisions of "Relationship between cosh, inverse Gudermannian, and sec"
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\cosh(\mathrm{gd}^{-1}(x))=\sec(x),$$ | $$\cosh(\mathrm{gd}^{-1}(x))=\sec(x),$$ | ||
where $\cosh$ is the [[cosh|hyperbolic cosine]], $\mathrm{gd}^{-1}$ is the [[inverse Gudermannian]], and $\sec$ is the [[secant]]. | where $\cosh$ is the [[cosh|hyperbolic cosine]], $\mathrm{gd}^{-1}$ is the [[inverse Gudermannian]], and $\sec$ is the [[secant]]. | ||
| − | + | ||
| − | + | ==Proof== | |
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| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:46, 8 June 2016
Theorem
The following formula holds: $$\cosh(\mathrm{gd}^{-1}(x))=\sec(x),$$ where $\cosh$ is the hyperbolic cosine, $\mathrm{gd}^{-1}$ is the inverse Gudermannian, and $\sec$ is the secant.
