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:
$$\cos(\mathrm{gd})(x)=\mathrm{sech}(x),$$
+
$$\cos(\mathrm{gd}(x))=\mathrm{sech}(x),$$
 
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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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: