Difference between revisions of "Relationship between cosine, Gudermannian, and sech"
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<strong>Theorem:</strong> The following formula holds: | <strong>Theorem:</strong> The following formula holds: | ||
| − | $$\cos(\mathrm{gd} | + | $$\cos(\mathrm{gd}(x))=\mathrm{sech}(x),$$ |
where $\cos$ denotes the [[cosine]], $\mathrm{gd}$ denotes the [[Gudermannian]], and $\mathrm{sech}$ denotes the [[sech|hyperbolic secant]]. | where $\cos$ denotes the [[cosine]], $\mathrm{gd}$ denotes the [[Gudermannian]], and $\mathrm{sech}$ denotes the [[sech|hyperbolic secant]]. | ||
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Revision as of 22:50, 25 August 2015
Theorem: The following formula holds: $$\cos(\mathrm{gd}(x))=\mathrm{sech}(x),$$ where $\cos$ denotes the cosine, $\mathrm{gd}$ denotes the Gudermannian, and $\mathrm{sech}$ denotes the hyperbolic secant.
Proof: █
