Điều kiện xác định:
$\begin{array}{l} \left\{ \begin{array}{l} \sin x + 3 \ge 0\\ 2{\cos ^2}x - 1 \ne 0 \end{array} \right. \Leftrightarrow 2{\cos ^2}x - 1 \ne 0\\ \left( { - 1 \le \sin x \le 1 \Rightarrow \sin x + 3 \ge 2 > 0} \right)\\ \Leftrightarrow \cos 2x \ne 0 \Leftrightarrow 2x \ne \dfrac{\pi }{2} + k\pi \\ \Leftrightarrow x \ne \dfrac{\pi }{4} + \dfrac{{k\pi }}{2}\left( {k \in \mathbb{Z}} \right)\\ D = \mathbb{R}\backslash \left\{ {\dfrac{\pi }{4} + \dfrac{{k\pi }}{2}|k \in \mathbb{Z}} \right\} \end{array}$
$\begin{array}{l}
y = \dfrac{4}{{\sqrt 3 \sin x\cos x}} = \dfrac{8}{{2\sqrt 3 \sin x\cos x}} = \dfrac{8}{{\sqrt 3 \sin 2x}}\\
- 1 \le \sin 2x \le 1 \Rightarrow - \sqrt 3 \le \sqrt 3 \sin 2x \le \sqrt 3 \\
\Rightarrow - \dfrac{8}{{\sqrt 3 }} \le y \le \dfrac{8}{{\sqrt 3 }}\\
\Rightarrow \max y = \dfrac{8}{{\sqrt 3 }},\min y = - \dfrac{8}{{\sqrt 3 }}
\end{array}$
