Giải phương trình $\sin 18x\cos 13x = \sin 9x\cos 4x$.

$\begin{array}{l}\,\,\,\,\,\sin 18x\cos 13x = \sin 9x\cos 4x\\ \Leftrightarrow \dfrac{1}{2}\left( {\sin 31x + \sin 5x} \right) = \dfrac{1}{2}\left( {\sin 13x + \sin 5x} \right)\\ \Leftrightarrow \sin 31x + \sin 5x = \sin 13x + \sin 5x\\ \Leftrightarrow \sin 31x = \sin 13x\\ \Leftrightarrow \left[ \begin{array}{l}31x = 13x + k2\pi \\31x = \pi  - 13x + k2\pi \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l}18x = k2\pi \\44x = \pi  + k2\pi \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l}x = \dfrac{{k\pi }}{9}\\x = \dfrac{\pi }{{44}} + \dfrac{{k\pi }}{{22}}\end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\end{array}$

Vậy nghiệm của phương trình là $x = \dfrac{{k\pi }}{9};\,\,x = \dfrac{\pi }{{44}} + \dfrac{{k\pi }}{{22}}\,\,\left( {k \in \mathbb{Z}} \right)$