Answer
$x=\frac{3\pi}{2}$
Work Step by Step
$cos(x+\frac{\pi}{6})-cos(x-\frac{\pi}{6})=1$
$cos~x~cos\frac{\pi}{6}-sin~x~sin\frac{\pi}{6}-(cos~x~cos\frac{\pi}{6}+sin~x~sin\frac{\pi}{6})=1$
$-2~sin~x~sin\frac{\pi}{6}=1$
$-2~sin~x~\frac{1}{2}=1$
$sin~x=-1$
$x=\frac{3\pi}{2}$
