Giải phương trình $si{n}^{2}x+sin2x.sin4x+sin3x.sin9x+sin4x.sin16x=1$

A. $x=-\frac{\mathrm{\pi }}{18}+\frac{k\mathrm{\pi }}{3}; x=\frac{5\mathrm{\pi }}{18}+\frac{k2\mathrm{\pi }}{9}$

B. $x=\pm \frac{\mathrm{\pi }}{18}+k2\mathrm{\pi }; x=\frac{5\mathrm{\pi }}{18}+\frac{k2\mathrm{\pi }}{3}$

C. $x=\frac{\mathrm{\pi }}{8}+\frac{k\mathrm{\pi }}{4}; x=\frac{\mathrm{\pi }}{18}+\frac{k2\mathrm{\pi }}{3}; x=\frac{5\mathrm{\pi }}{18}+\frac{k2\mathrm{\pi }}{3}$

D. $x=\frac{\mathrm{\pi }}{8}+\frac{k\mathrm{\pi }}{4}; x=\frac{\mathrm{\pi }}{18}+\frac{k\mathrm{\pi }}{18}; x=-\frac{5\mathrm{\pi }}{18}+\frac{k\mathrm{\pi }}{3}$

A. $x=\frac{\mathrm{\pi }}{2}+k\mathrm{\pi }, \mathrm{x}=\pm \frac{1}{5}\arccos \frac{1+\sqrt{17}}{8}+\mathrm{k\pi }, \mathrm{x}=\pm \frac{1}{5}\arccos \frac{1-\sqrt{17}}{8}+\mathrm{k\pi }$

B. $\mathrm{x}=\pm \frac{1}{2}\arccos \frac{1+\sqrt{17}}{8}+\mathrm{k\pi }, \mathrm{x}=\pm \frac{1}{2}\arccos \frac{1-\sqrt{17}}{8}+\mathrm{k\pi }$

C. $x=\frac{\mathrm{\pi }}{2}+k\mathrm{\pi }, \mathrm{x}=\pm \frac{1}{2}\arccos \frac{1+\sqrt{15}}{7}+\mathrm{k\pi }, \mathrm{x}=\pm \frac{1}{2}\arccos \frac{1-\sqrt{15}}{7}+\mathrm{k\pi }$

D. $x=\frac{\mathrm{\pi }}{2}+k\mathrm{\pi }, \mathrm{x}=\pm \frac{1}{2}\arccos \frac{1+\sqrt{17}}{8}+\mathrm{k\pi }, \mathrm{x}=\pm \frac{1}{2}\arccos \frac{1-\sqrt{17}}{8}+\mathrm{k\pi }$

A. $x=\frac{\mathrm{\pi }}{6}+\frac{k2\mathrm{\pi }}{3}, x=\pm \frac{2\mathrm{\pi }}{3}+2k\mathrm{\pi }$

B. $x=\frac{k2\mathrm{\pi }}{7}, x=\frac{\mathrm{\pi }}{3}+\frac{\mathrm{k}2\mathrm{\pi }}{3}, x=\pm \frac{2\mathrm{\pi }}{3}+k2\mathrm{\pi }$

C. $x=\frac{k2\mathrm{\pi }}{3}, x=\frac{\mathrm{\pi }}{3}+\frac{\mathrm{k}2\mathrm{\pi }}{3}, x=\pm \frac{\mathrm{\pi }}{7}+k2\mathrm{\pi }$

D. $x=\frac{k2\mathrm{\pi }}{7}+k\mathrm{\pi }, x=\frac{2\mathrm{\pi }}{3}+\frac{\mathrm{k}2\mathrm{\pi }}{3}$ 

A. $x=-\frac{\mathrm{\pi }}{4}+k\mathrm{\pi }; \mathrm{x}=\frac{\mathrm{\pi }}{6}+\mathrm{k}2\mathrm{\pi }; \mathrm{x}=\frac{5\mathrm{\pi }}{6}+\mathrm{k}2\mathrm{\pi }; \mathrm{x}=-\frac{\mathrm{\pi }}{2}+\mathrm{k}2\mathrm{\pi }\left(\mathrm{k}\in \mathrm{Z}\right)$

B. $x=\frac{\mathrm{\pi }}{4}+k2\mathrm{\pi }; \mathrm{x}=-\frac{\mathrm{\pi }}{6}+\mathrm{k}2\mathrm{\pi }; \mathrm{x}=\frac{5\mathrm{\pi }}{6}+\mathrm{k\pi }; \mathrm{x}=-\frac{\mathrm{\pi }}{2}+\mathrm{k\pi }\left(\mathrm{k}\in \mathrm{Z}\right)$

C. $x=\pm \frac{\mathrm{\pi }}{6}+k2\mathrm{\pi }; \mathrm{x}=\frac{5\mathrm{\pi }}{6}+\mathrm{k}2\mathrm{\pi }; \mathrm{x}=-\frac{\mathrm{\pi }}{2}+\mathrm{k}2\mathrm{\pi }\left(\mathrm{k}\in \mathrm{Z}\right)$

D. $x=-\frac{\mathrm{\pi }}{8}+k\mathrm{\pi }; \mathrm{x}=\frac{\mathrm{\pi }}{6}+\mathrm{k\pi }; \mathrm{x}=-\frac{5\mathrm{\pi }}{6}+\frac{\mathrm{k\pi }}{6}; \mathrm{x}=-\frac{\mathrm{\pi }}{2}+\frac{k\mathrm{\pi }}{6}\left(\mathrm{k}\in \mathrm{Z}\right)$

A. $x=k\mathrm{\pi }, \mathrm{x}=\frac{\mathrm{\pi }}{6}+\frac{\mathrm{k\pi }}{3}, \mathrm{x}=\frac{\mathrm{\pi }}{12}+\mathrm{k\pi }, \mathrm{x}=\frac{5\mathrm{\pi }}{7}+\mathrm{k\pi }$

B. $x=k2\mathrm{\pi }, \mathrm{x}=\frac{\mathrm{\pi }}{3}+\frac{k2\pi }{3}, \mathrm{x}=\frac{\mathrm{\pi }}{12}+\mathrm{k\pi }, \mathrm{x}=\frac{5\mathrm{\pi }}{12}+\mathrm{k\pi }$

C. $x=k\mathrm{\pi }, \mathrm{x}=\frac{\mathrm{\pi }}{3}+\frac{k2\pi }{3}, \mathrm{x}=\frac{\mathrm{\pi }}{12}+\mathrm{k\pi }, \mathrm{x}=\frac{5\mathrm{\pi }}{12}+\mathrm{k\pi }$

D. $x=k2\mathrm{\pi }, \mathrm{x}=\frac{\mathrm{\pi }}{6}+\frac{k2\pi }{3}, \mathrm{x}=\frac{\mathrm{\pi }}{12}+\mathrm{k\pi }, \mathrm{x}=\frac{7\mathrm{\pi }}{12}+\mathrm{k\pi }$

A. $\left\{\begin{array}{l}x=\pi +k\pi \\ y=-\frac{\pi }{3}-k\pi \end{array}\right.$

B. $\left\{\begin{array}{l}x=\frac{2\pi }{3}+k\pi \\ y=-k\pi \end{array}\right.$

C. $\left\{\begin{array}{l}x=\frac{\pi }{3}+k\pi \\ y=\frac{\pi }{3}-k\pi \end{array}\right.$

D. $\left\{\begin{array}{l}x=\frac{5\pi }{6}+k\pi \\ y=-\frac{\pi }{6}-k\pi \end{array}\right.$