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