Difference between revisions of "Relationship between csch, inverse Gudermannian, and cot"

From specialfunctionswiki
Jump to: navigation, search
(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\mat...")
 
 
Line 1: Line 1:
<div class="toccolours mw-collapsible mw-collapsed">
+
==Theorem==
<strong>[[Relationship between csch, inverse Gudermannian, and cot|Theorem]]:</strong> The following formula holds:
+
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]].
<div class="mw-collapsible-content">
+
 
<strong>Proof:</strong> █
+
==Proof==
</div>
+
 
</div>
+
==References==
 +
 
 +
[[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.

Proof

References