cos(y+z) + cos(z+x) + cos(x+y) = a
Source: IMO Longlist 1989, Problem 70
September 18, 2008
trigonometrycomplex numbersalgebra unsolvedalgebra
Problem Statement
Given that \frac{\cos(x) \plus{} \cos(y) \plus{} \cos(z)}{\cos(x\plus{}y\plus{}z)} \equal{} \frac{\sin(x)\plus{} \sin(y) \plus{} \sin(z)}{\sin(x \plus{} y \plus{} z)} \equal{} a, show that \cos(y\plus{}z) \plus{} \cos(z\plus{}x) \plus{} \cos(x\plus{}y) \equal{} a.