Phương trình $\displaystyle \sin x+\cos x=1-\frac{1}{2}\sin 2x$có nghiệm là
A. $\displaystyle \left[ \begin{array}{l}x=\frac{\pi }{6}+k\frac{\pi }{2}\\x=k\frac{\pi }{4}\end{array} \right.$
B. $\displaystyle \left[ \begin{array}{l}x=\frac{\pi }{8}+k\pi \\x=k\frac{\pi }{2}\end{array} \right.$
C. $\displaystyle \left[ \begin{array}{l}x=\frac{\pi }{4}+k\pi \\x=k\pi \end{array} \right.$
D. $\displaystyle \left[ \begin{array}{l}x=\frac{\pi }{2}+k2\pi \\x=k2\pi \end{array} \right.$