\(\Leftrightarrow\frac{1}{2}sin3x+\frac{1}{2}sinx=\frac{1}{2}sin11x+\frac{1}{2}sin3x\)
\(\Leftrightarrow sin11x=sinx\)
\(\Leftrightarrow\left[{}\begin{matrix}11x=x+k2\pi\\11x=\pi-x+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{k\pi}{5}\\x=\frac{\pi}{12}+\frac{k\pi}{6}\end{matrix}\right.\)