Phương trình

Câu hỏi: Phương trình ${\sin }^{3}x+{\cos }^{3}x=1-\frac{1}{2}\sin 2x$ có nghiệm là

A.$\left[\begin{array}{l}x=\frac{\pi }{4}+k\pi \\ x=k\pi \end{array}\right.,k\in \mathbb{Z}.$

B.$\left[\begin{array}{l}x=\frac{\pi }{2}+k2\pi \\ x=k2\pi \end{array}\right.,k\in \mathbb{Z}.$

C.$\left[\begin{array}{l}x=\frac{3\pi }{4}+k\pi \\ x=k\frac{\pi }{2}\end{array}\right.,k\in \mathbb{Z}.$

D.$\left[\begin{array}{l}x=\frac{3\pi }{2}+k\pi \\ x=\left(2k+1\right)\pi \end{array}\right.,k\in \mathbb{Z}.$