Question 37
(HUN 4) (IMO 2) If $a_1,a_2,\ldots,a_n$ 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 $y\equiv0$.
$$y=\cos(a_1+x)+2\cos(a_2+x)+\cdots+n\cos(a_n+x)$$
has two zeros $x_1$ and $x_2$ whose difference is not a multiple of $\pi$, prove that $y\equiv0$.