# Law of Tangents

Law of tangents is a less known formula when compared with Laws of sines and cosines. Law of tangents establishes a ratio relationship between the sum and difference of two sides of a triangle to the tangents of half the sum and differences of the angles opposite to the sides. It can also be used to solve triangles when two sides and the included angle are given. Thus in SAS situations, Law of tangents can be used instead of Law of cosines. Like laws of sines and cosines law of tangents is also used in proving identities related to the measures of a triangle.**The law of tangents for the ΔABC consists of three formulas as follows:**

1. $\frac{a+b}{a-b}$ = $\frac{tan\frac{A+B}{2}}{tan\frac{A-B}{2}}$

2. $\frac{b+c}{b-c}$ = $\frac{tan\frac{B+C}{2}}{tan\frac{B-C}{2}}$

3. $\frac{c+a}{c-a}$ = $\frac{tan\frac{C+A}{2}}{tan\frac{C-A}{2}}$

Let us look into the proof of law of tangents and solve few problems using this property.