$\begin{array}{l} y = \dfrac{2}{{3 + \cos x}}\\ - 1 \le \cos x \le 1\\ \Rightarrow 2 \le 3 + \cos x \le 4\\ \Rightarrow \dfrac{1}{2} \le y \le 1\\ \Rightarrow \left\{ \begin{array}{l} \min y = \dfrac{1}{2} \Rightarrow \cos x = 1\\ \max y = 1 \Rightarrow \cos x = - 1 \end{array} \right.\\ \Rightarrow \left\{ \begin{array}{l} \min y = \dfrac{1}{2} \Rightarrow x = k2\pi \\ \max y = 1 \Rightarrow x = \pi + k2\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right) \end{array}$
