Difference between revisions of "Relationship between cot, Gudermannian, and csch"
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\cot(\mathrm{gd}(x))=\mathrm{csch}(x),$$ | $$\cot(\mathrm{gd}(x))=\mathrm{csch}(x),$$ | ||
where $\cot$ is the [[cotangent]], $\mathrm{gd}$ is the [[Gudermannian]], and $\mathrm{csch}$ is the [[csch|hyperbolic cosecant]]. | where $\cot$ is the [[cotangent]], $\mathrm{gd}$ is the [[Gudermannian]], and $\mathrm{csch}$ is the [[csch|hyperbolic cosecant]]. | ||
| − | + | ||
| − | + | ==Proof== | |
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| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:48, 8 June 2016
Theorem
The following formula holds: $$\cot(\mathrm{gd}(x))=\mathrm{csch}(x),$$ where $\cot$ is the cotangent, $\mathrm{gd}$ is the Gudermannian, and $\mathrm{csch}$ is the hyperbolic cosecant.
