ĐK: $\sin x-\cos x \ne 0$
$\Leftrightarrow \sqrt2(\dfrac{1}{\sqrt2}\sin x -\dfrac{1}{\sqrt2}\cos x)\ne 0$
$\Leftrightarrow \sin(x-\dfrac{\pi}{4})\ne 0$
$\Leftrightarrow x-\dfrac{\pi}{4}\ne k\pi$
$\Leftrightarrow x\ne \dfrac{\pi}{4}+k\pi$
$D=\mathbb{R}$ \ $\{\dfrac{\pi}{4}+k\pi\}$
$\rightarrow D$