Difference between revisions of "Relationship between csc, Gudermannian, and coth"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\csc(\mathrm{gd}(x))=\mathrm{coth}(x),$$ where $\csc$ is the co...") |
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| − | <strong>Theorem:</strong> The following formula holds: | + | <strong>[[Relationship between csc, Gudermannian, and coth|Theorem]]:</strong> The following formula holds: |
$$\csc(\mathrm{gd}(x))=\mathrm{coth}(x),$$ | $$\csc(\mathrm{gd}(x))=\mathrm{coth}(x),$$ | ||
| − | where $\csc$ is the [[cosecant]], $\mathrm{gd}$ is the Gudermannian, and $\mathrm{coth}$ is the [[coth|hyperbolic cotangent]]. | + | where $\csc$ is the [[cosecant]], $\mathrm{gd}$ is the [[Gudermannian]], and $\mathrm{coth}$ is the [[coth|hyperbolic cotangent]]. |
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
</div> | </div> | ||
</div> | </div> | ||
Revision as of 22:58, 25 August 2015
Theorem: The following formula holds: $$\csc(\mathrm{gd}(x))=\mathrm{coth}(x),$$ where $\csc$ is the cosecant, $\mathrm{gd}$ is the Gudermannian, and $\mathrm{coth}$ is the hyperbolic cotangent.
Proof: █
