Difference between revisions of "Relationship between sinh, inverse Gudermannian, and tan"
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\sinh(\mathrm{gd}^{-1}(x))=\tan(x),$$ | $$\sinh(\mathrm{gd}^{-1}(x))=\tan(x),$$ | ||
where $\sinh$ is the [[sinh|hyperbolic sine]], $\mathrm{gd}^{-1}$ is the [[inverse Gudermannian]], and $\tan$ is the [[tangent]]. | where $\sinh$ is the [[sinh|hyperbolic sine]], $\mathrm{gd}^{-1}$ is the [[inverse Gudermannian]], and $\tan$ is the [[tangent]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:37, 8 June 2016
Theorem
The following formula holds: $$\sinh(\mathrm{gd}^{-1}(x))=\tan(x),$$ where $\sinh$ is the hyperbolic sine, $\mathrm{gd}^{-1}$ is the inverse Gudermannian, and $\tan$ is the tangent.
