Giải phương trình ${\sin ^2}x + \sin 2x\sin 4x + \sin 3x\sin 9x + \sin 4x\sin 16x = 1$.

1

2

3

4

$x =  - \dfrac{\pi }{6} + k2\pi .$

$x = \dfrac{\pi }{6} + k2\pi .$

$x = \dfrac{\pi }{6} + k\pi .$

$x = \dfrac{{5\pi }}{6} + k2\pi .$

$k2\pi .$

$\dfrac{\pi }{2} + k2\pi .$

$\pi  + k2\pi .$

$\pi  + k2\pi .$

2

3

1

4

$\left[ \begin{array}{l}x = \dfrac{\pi }{6} + k2\pi \\x = {\rm{arctan}}\left( { - 2} \right) + k2\pi \end{array} \right.$    

$\left[ \begin{array}{l}x = \dfrac{\pi }{3} + k\pi \\x = {\rm{arctan}}\left( { - 2} \right) + k\pi \end{array} \right.$

$\left[ \begin{array}{l}x = \dfrac{\pi }{6} + k\pi \\x = {\rm{arctan}}\left( { - 2} \right) + k\pi \end{array} \right.$

$\left[ \begin{array}{l}x = \dfrac{\pi }{6} + k\pi \\x =  - {\rm{arctan}}\left( 2 \right) + k\pi \end{array} \right.$

$m \ge  - \dfrac{2}{3}.$

$\dfrac{2}{5} \le m \le 2.$

$- \dfrac{2}{3} \le m \le 2.$

$m \le  - \dfrac{2}{3}.$

$\dfrac{{1150}}{3}\pi$.

$\dfrac{{570}}{3}\pi$.

$\dfrac{{880}}{3}\pi$.

$\dfrac{{875}}{3}\pi$.