Difference between revisions of "Relationship between cosine, Gudermannian, and sech"

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==Theorem==
<strong>[[Relationship between cosine, Gudermannian, and sech|Theorem]]:</strong> The following formula holds:
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The following formula holds:
 
$$\cos(\mathrm{gd}(x))=\mathrm{sech}(x),$$
 
$$\cos(\mathrm{gd}(x))=\mathrm{sech}(x),$$
 
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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<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]]

Latest revision as of 07:42, 8 June 2016

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

References