b,
ĐK: $\sin x\ne 0; \cos x\ne 0$
$\Leftrightarrow \sin2x=2\sin x\cos x\ne 0$
$\Leftrightarrow 2x\ne 0$
$\Leftrightarrow x\ne \dfrac{k\pi}{2}$
$\to D=\mathbb{R}$ \ $\{\dfrac{k\pi}{2}\}$
d,
ĐK: $\sin(2x+\dfrac{\pi}{4})\ne 0$
$\Leftrightarrow 2x+\dfrac{\pi}{4}\ne k\pi$
$\Leftrightarrow x\ne \dfrac{-\pi}{8}+\dfrac{k\pi}{2}$
$\to D=\mathbb{R}$ \ $\{\dfrac{-\pi}{8}+\dfrac{k\pi}{2}\}$