Difference between revisions of "Relationship between tangent, Gudermannian, and sinh"

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==Theorem==
<strong>[[Relationship between tangent, Gudermannian, and sinh|Theorem]]:</strong> The following formula holds:
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The following formula holds:
 
$$\tan(\mathrm{gd}(x))=\sinh(x),$$
 
$$\tan(\mathrm{gd}(x))=\sinh(x),$$
 
where $\tan$ denotes the [[tangent]], $\mathrm{gd}$ denotes the [[Gudermannian]], and $\sinh$ denotes the [[sinh|hyperbolic sine]].
 
where $\tan$ denotes the [[tangent]], $\mathrm{gd}$ denotes the [[Gudermannian]], and $\sinh$ denotes the [[sinh|hyperbolic sine]].
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<strong>Proof:</strong> █
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==Proof==
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==References==
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[[Category:Theorem]]
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[[Category:Unproven]]

Revision as of 07:36, 8 June 2016

Theorem

The following formula holds: $$\tan(\mathrm{gd}(x))=\sinh(x),$$ where $\tan$ denotes the tangent, $\mathrm{gd}$ denotes the Gudermannian, and $\sinh$ denotes the hyperbolic sine.

Proof

References