Let , where . If , then may be equal…

MATHEMATICS · Multi correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let

f(x)=\cos(a_1+x)+\frac{1}{2}\cos(a_2+x)+\frac{1}{2^2}\cos(a_3+x)+\dots+\frac{1}{2^{n-1}}\cos(a_n+x)

, where

a_1,a_2,\dots,a_n\in\mathbb{R}

. If

f(x_1)=f(x_2)=0

, then

|x_2-x_1|

may be equal to: (1)

\pi

(2)

2\pi

(3)

3\pi

(4)

\frac{\pi}{2}