Giải phương trình

Câu hỏi: Giải phương trình $\sin (2x+\frac{\mathrm{\pi }}{3})=-\frac{1}{2}$

A. $\left\{\begin{array}{l}x=-\frac{\mathrm{\pi }}{4}+k\mathrm{\pi }\\ x=\frac{5\mathrm{\pi }}{12}+k\mathrm{\pi }\end{array}\right.(k\in \mathrm{ℝ})$

B. $\left\{\begin{array}{l}x=\frac{\mathrm{\pi }}{4}+k\mathrm{\pi }\\ x=\frac{5\mathrm{\pi }}{12}+k\mathrm{\pi }\end{array}\right.(k\in \mathrm{ℝ})$

C. $\left\{\begin{array}{l}x=\frac{\mathrm{\pi }}{4}+k\mathrm{\pi }\\ x=\frac{\mathrm{\pi }}{12}+k\mathrm{\pi }\end{array}\right.(k\in \mathrm{ℝ})$

D. $\left\{\begin{array}{l}x=-\frac{\mathrm{\pi }}{4}+k\mathrm{\pi }\\ x=\frac{\mathrm{\pi }}{12}+k\mathrm{\pi }\end{array}\right.(k\in \mathrm{ℝ})$