Difference between revisions of "Relationship between secant, Gudermannian, and cosh"
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| − | <strong>Theorem:</strong> The following formula holds: | + | <strong>[[Relationship between secant, Gudermannian, and cosh|Theorem]]:</strong> The following formula holds: |
$$\sec(\mathrm{gd}(x))=\cosh(x),$$ | $$\sec(\mathrm{gd}(x))=\cosh(x),$$ | ||
where $\sec$ denotes the [[secant]], $\mathrm{gd}$ denotes the [[Gudermannian]], and $\cosh$ denotes the [[cosh|hyperbolic cosine]]. | where $\sec$ denotes the [[secant]], $\mathrm{gd}$ denotes the [[Gudermannian]], and $\cosh$ denotes the [[cosh|hyperbolic cosine]]. | ||
Revision as of 22:59, 25 August 2015
Theorem: The following formula holds: $$\sec(\mathrm{gd}(x))=\cosh(x),$$ where $\sec$ denotes the secant, $\mathrm{gd}$ denotes the Gudermannian, and $\cosh$ denotes the hyperbolic cosine.
Proof: █
