Question 2
Let $a_1,a_2,\ldots,a_n$ be real constants and
$$y(x)=\cos(a_1+x)+\frac{\cos(a_2+x)}2+\frac{\cos(a_3+x)}{2^2}+\cdots+\frac{\cos(a_n+x)}{2^{n-1}}.$$
If $x_1,x_2$ are real and $y(x_1)=y(x_2)=0$, prove that $x_1-x_2=m\pi$ for some integer $m$.
$$y(x)=\cos(a_1+x)+\frac{\cos(a_2+x)}2+\frac{\cos(a_3+x)}{2^2}+\cdots+\frac{\cos(a_n+x)}{2^{n-1}}.$$
If $x_1,x_2$ are real and $y(x_1)=y(x_2)=0$, prove that $x_1-x_2=m\pi$ for some integer $m$.