Theo BĐT Bunhiacopxki ta có:
\(\begin{array}{l}
{\left( {\cos x + \sqrt {2 - {{\cos }^2}x} } \right)^2} \le \left( {1 + 1} \right)\left( {{{\cos }^2}x + 2 - {{\cos }^2}c} \right)\\
\Leftrightarrow {y^2} \le 4\\
\Rightarrow {y_{\max }} = 2 \Leftrightarrow \cos x = \sqrt {2 - {{\cos }^2}x} \Rightarrow \cos x = 1 \Leftrightarrow x = k2\pi
\end{array}\)
