IMO 1969 LL HUN37

Origin: HUN

Problem

If a1, a2, . . . , an are real constants, and if y = cos(a1 + x) + 2 cos(a2 + x) + \cdot \cdot \cdot + n cos(an + x) has two zeros x1 and x2 whose difference is not a multiple of \pi, prove that y \equiv0.