# 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]]. | ||

− | + | ||

− | + | ==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.