$y=\dfrac{\cos2x-1}{\cos(2x-1)}$
ĐK: $\cos(2x-1)\ne 0$
$\Leftrightarrow 2x-1\ne \dfrac{\pi}{2}+k\pi$
$\Leftrightarrow x\ne \dfrac{1}{2}+\dfrac{\pi}{4}+\dfrac{k\pi}{2}$
Vậy:
$D=\mathbb{R}$ \ $\Big\{\dfrac{1}{2}+\dfrac{\pi}{4}+\dfrac{k\pi}{2}| k\in\mathbb{Z}\Big\}$