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Mollweide's formula
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Mollweide's formula : ウィキペディア英語版
Mollweide's formula

In trigonometry, Mollweide's formula, sometimes referred to in older texts as Mollweide's equations,〔Ernest Julius Wilczynski, ''Plane Trigonometry and Applications'', Allyn and Bacon, 1914, page 102〕 named after Karl Mollweide, is a set of two relationships between sides and angles in a triangle.〔Michael Sullivan, ''Trigonometry'', Dellen Publishing Company, 1988, page 243.〕 It can be used to check solutions of triangles.〔Ernest Julius Wilczynski, ''Plane Trigonometry and Applications'', Allyn and Bacon, 1914, page 105〕
Let ''a'', ''b'', and ''c'' be the lengths of the three sides of a triangle.
Let ''α'', ''β'', and ''γ'' be the measures of the angles opposite those three sides respectively. Mollweide's formula states that
: \frac = \frac\right)}\right)}
and
: \frac = \frac\right)}\right)}.
Each of these identities uses all six parts of the triangle—the three angles and the lengths of the three sides.
==See also==

* Law of sines
* Law of cosines
* Law of tangents
* Law of cotangents
m

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