# Tangent formula

From Encyclopedia of Mathematics

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.

#### Comments

#### References

[a1] | M. Berger, "Geometry" , 1–2 , Springer (1987) (Translated from French) |

[a2] | E.W. Hobson, "Plane trigonometry" , Cambridge Univ. Press (1925) pp. 158 |

**How to Cite This Entry:**

Tangent formula.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Tangent_formula&oldid=31425

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article