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== | |
+ | |||
+ | [[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.