MathDB

3

Part of 1991 India National Olympiad

Problems(1)

Simple trignometry

Source: INMO 1991 Problem 3

10/3/2005
Given a triangle ABCABC let \begin{eqnarray*} x &=& \tan\left(\dfrac{B-C}{2}\right) \tan \left(\dfrac{A}{2}\right) \\ y &=& \tan\left(\dfrac{C-A}{2}\right) \tan \left(\dfrac{B}{2}\right) \\ z &=& \tan\left(\dfrac{A-B}{2}\right) \tan \left(\dfrac{C}{2}\right). \end{eqnarray*} Prove that x+y+z+xyz=0x+ y + z + xyz = 0.
trigonometry