Đáp án:
3 số lập thành CSC thì:
$\begin{array}{l}
\Rightarrow 2{\sin ^2}2x = {\mathop{\rm s}\nolimits} {\rm{inx}} + 1 - \sin 7x\\
\Rightarrow 1 - 2{\sin ^2}2x = \sin 7x - {\mathop{\rm s}\nolimits} {\rm{inx}}\\
\Rightarrow \cos 4x = 2\cos 4x.\sin 3x\\
\Rightarrow \cos 4x.\left( {1 - 2\sin 3x} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
\cos 4x = 0\\
sin3x = \frac{1}{2}
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
4x = \frac{\pi }{2} + k\pi \\
3x = \frac{\pi }{6} + k2\pi \\
3x = \frac{{5\pi }}{6} + k2\pi
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x = \frac{\pi }{8} + \frac{{k\pi }}{2}\\
x = \frac{\pi }{{18}} + \frac{{k2\pi }}{3}\\
x = \frac{{5\pi }}{{18}} + \frac{{k2\pi }}{3}
\end{array} \right.
\end{array}$
