![(HUN 4)](/media/m/4/5/9/459d0a884c85c3bf12b5b59b6eebff76.png)
IMO2 If
![a_1, a_2, . . . , a_n](/media/m/2/f/8/2f81fcfaa676f54a88ff36aa101db73d.png)
are real constants, and if
![y = \cos(a_1 + x) +2\cos(a_2+x)+ \cdots+ n \cos(a_n + x)](/media/m/0/8/5/0854d095cfa1271bbc4d9bb93302f825.png)
has two zeros
![x_1](/media/m/9/2/a/92aefd356eeab9982f45f21fb206a2ef.png)
and
![x_2](/media/m/a/a/1/aa16f4edacb7b534405242617406658f.png)
whose difference is not a multiple of
![\pi](/media/m/6/d/c/6dc45296009278a7c7756c5f81a379fb.png)
, prove that
%V0
$(HUN 4)$IMO2 If $a_1, a_2, . . . , a_n$ are real constants, and if $y = \cos(a_1 + x) +2\cos(a_2+x)+ \cdots+ n \cos(a_n + x)$ has two zeros $x_1$ and $x_2$ whose difference is not a multiple of $\pi$, prove that $y = 0.$