Difference between revisions of "Relationship between csch, inverse Gudermannian, and cot"
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− | + | ==Theorem== | |
− | + | The following formula holds: | |
$$\mathrm{csch}(\mathrm{gd}^{-1}(x))=\cot(x),$$ | $$\mathrm{csch}(\mathrm{gd}^{-1}(x))=\cot(x),$$ | ||
where $\mathrm{csch}$ is the [[csch|hyperbolic cosecant]], $\mathrm{gd}^{-1}$ is the [[inverse Gudermannian]], and $\cot$ is the [[cotangent]]. | where $\mathrm{csch}$ is the [[csch|hyperbolic cosecant]], $\mathrm{gd}^{-1}$ is the [[inverse Gudermannian]], and $\cot$ is the [[cotangent]]. | ||
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− | + | ==Proof== | |
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− | + | ==References== | |
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+ | [[Category:Theorem]] | ||
+ | [[Category:Unproven]] |
Latest revision as of 07:49, 8 June 2016
Theorem
The following formula holds: $$\mathrm{csch}(\mathrm{gd}^{-1}(x))=\cot(x),$$ where $\mathrm{csch}$ is the hyperbolic cosecant, $\mathrm{gd}^{-1}$ is the inverse Gudermannian, and $\cot$ is the cotangent.