Hướng dẫn giải: 

$\begin{align}  & \sqrt{2}\left( \sin x+\cos x \right)=\frac{1}{2}\cos 2x \\ & \Leftrightarrow 2\sqrt{2}(\sin x+\cos x)-({{\cos }^{2}}x-{{\sin }^{2}}x)=0 \\ & \Leftrightarrow \left[ \begin{matrix}   \sin x+\cos x=0  \\   \cos x-\sin x=2\sqrt{2}(loai)  \\\end{matrix} \right. \\ & \Rightarrow \cos (x-\frac{\pi }{4})=0 \\ & \Leftrightarrow x=\frac{3}{4}\pi +k\pi ,k\in \mathbb{Z} \\ & x\in (1,9) \\ & \Rightarrow k=\{0;1;2\} \\\end{align}$

Chọn C.