Difference between revisions of "Relationship between sech, inverse Gudermannian, and cos"
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\mathrm{sech}(\mathrm{gd}^{-1}(x))=\cos(x),$$ | $$\mathrm{sech}(\mathrm{gd}^{-1}(x))=\cos(x),$$ | ||
where $\mathrm{sech}$ is the [[sech|hyperbolic secant]], $\mathrm{gd}^{-1}$ is the [[inverse Gudermannian]], and $\cos$ is the [[cosine]]. | where $\mathrm{sech}$ is the [[sech|hyperbolic secant]], $\mathrm{gd}^{-1}$ is the [[inverse Gudermannian]], and $\cos$ is the [[cosine]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:42, 8 June 2016
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.
