tìm min của hàm số y=2/cosx + 1

tìm min của hàm số y=2/cosx + 1

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

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