Difference between revisions of "Relationship between tangent, Gudermannian, and sinh"
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| − | + | ==Theorem== | |
| − | + | 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]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[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.
