Đáp án:
\(\left[ \begin{array}{l}
x = \dfrac{{k\pi }}{2}\\
x = \dfrac{{4\pi }}{9} + k\pi
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\sin \left( {3x + 10} \right) + \sin \left( {x - 10} \right) = 0\\
\to 2\sin \left( {\dfrac{{3x + 10 + x - 10}}{2}} \right).\cos \left( {\dfrac{{3x + 10 - x + 10}}{2}} \right) = 0\\
\to 2\sin \left( {2x} \right).\cos \left( {x + 10} \right) = 0\\
\to \left[ \begin{array}{l}
\sin \left( {2x} \right) = 0\\
\cos \left( {x + 10} \right) = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
2x = k\pi \\
x + \dfrac{\pi }{{18}} = \dfrac{\pi }{2} + k\pi
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{{k\pi }}{2}\\
x = \dfrac{{4\pi }}{9} + k\pi
\end{array} \right.\left( {k \in Z} \right)
\end{array}\)
