\[\begin{array}{l}
y = \frac{2}{{\cos x + 1}} = \frac{2}{{2{{\cos }^2}\frac{x}{2} - 1 + 1}} = \frac{2}{{2{{\cos }^2}\frac{x}{2}}} = \frac{1}{{{{\cos }^2}\frac{x}{2}}}\\
Ta\,\,co:\,\,\,0 < {\cos ^2}\frac{x}{2} \le 1\\
\Rightarrow \frac{1}{{{{\cos }^2}\frac{x}{2}}} \ge 1\\
\Rightarrow Min\,\,y = 1\,\,khi\,\,\,{\cos ^2}\frac{x}{2} = 1 \Leftrightarrow \sin \frac{x}{2} = 0\\
\Leftrightarrow \frac{x}{2} = k\pi \Leftrightarrow x = k2\pi \,\,\left( {k \in Z} \right).
\end{array}\]
