MathNet 2008-part-02 — 165 problems (EN–VI) Question 160

Prove that $\frac{\tan\alpha}{\tan\beta} = \frac{a^2+c^2-b^2}{b^2+c^2-a^2}$ for every triangle $ABC$ ($a, b, c$ and $\alpha, \beta$ are the sides and the angles in the triangle, respectively).