Tangent formula

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A formula establishing the dependence between the lengths of two sides of a plane triangle and the tangents of the halved sum and the halved difference of the opposite angles. The tangent formula has the form

$$\frac{a-b}{a+b}=\frac{\tan\frac 12(A-B)}{\tan\frac 12(A+B)}.$$

Sometimes the tangent formula is called the Regiomontanus formula, after the scholar who established this formula in the second half of the 15th century.



[a1] M. Berger, "Geometry" , 1–2 , Springer (1987) (Translated from French)
[a2] E.W. Hobson, "Plane trigonometry" , Cambridge Univ. Press (1925) pp. 158
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Tangent formula. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article