ĐK: $\cos\left(\dfrac{\pi}{6}-\dfrac{3x}{4}\right)\ne 1$
$\to \cos\left( \dfrac{3x}{4}-\dfrac{\pi}{6}\right)\ne 1$
$\to\dfrac{3x}{4}-\dfrac{\pi}{6}\ne k2\pi$
$\to x\ne \dfrac{2\pi}{9}+\dfrac{k8\pi}{3}$
Vậy $D=\mathbb{R}$ \ $\left\{ \dfrac{2\pi}{9}+\dfrac{k8\pi}{3}\right\}$