7.
\(\Leftrightarrow\dfrac{\sqrt{3}}{2}cos3x+\dfrac{1}{2}sin3x=\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow cos\left(3x-\dfrac{\pi}{6}\right)=cos\left(\dfrac{\pi}{4}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-\dfrac{\pi}{6}=\dfrac{\pi}{4}+k2\pi\\3x-\dfrac{\pi}{6}=-\dfrac{\pi}{4}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5\pi}{36}+\dfrac{k2\pi}{3}\\x=-\dfrac{\pi}{36}+\dfrac{k2\pi}{3}\end{matrix}\right.\)
9.
\(\Leftrightarrow3sin3x-\sqrt{3}cos9x=1+3sin3x-sin9x\)
\(\Leftrightarrow sin9x-\sqrt{3}cos9x=1\)
\(\Leftrightarrow\dfrac{1}{2}sin9x-\dfrac{\sqrt{3}}{2}cos9x=\dfrac{1}{2}\)
\(\Leftrightarrow sin\left(9x-\dfrac{\pi}{3}\right)=sin\left(\dfrac{\pi}{6}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}9x-\dfrac{\pi}{3}=\dfrac{\pi}{6}+k2\pi\\9x-\dfrac{\pi}{3}=\dfrac{5\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{18}+\dfrac{k2\pi}{9}\\x=\dfrac{7\pi}{54}+\dfrac{k2\pi}{9}\end{matrix}\right.\)
