$y=\dfrac{2017\tan2x}{-(\cos^2x-\sin^2x)}$
$=\dfrac{2017.\dfrac{\sin2x}{\cos2x}}{-\cos2x}$
$=\dfrac{-2017\sin2x}{\cos^22x}$
ĐK: $\cos2x\ne 0$
$\to 2x\ne \dfrac{\pi}{2}+k\pi$
$\to x\ne \dfrac{\pi}{4}+\dfrac{k\pi}{2}$
Vậy $D=\mathbb{R}$ \ $\Big\{ \dfrac{\pi}{4}+\dfrac{k\pi}{2}\Big| k\in\mathbb{Z}\Big\}$