g, \(3sinx-1=4sin^3x+\sqrt{3}cos3x\)
\(\Leftrightarrow sin3x-\sqrt{3}cos3x=1\)
\(\Leftrightarrow\dfrac{1}{2}sin3x-\dfrac{\sqrt{3}}{2}cos3x=\dfrac{1}{2}\)
\(\Leftrightarrow sin\left(3x-\dfrac{\pi}{3}\right)=\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-\dfrac{\pi}{3}=\dfrac{\pi}{6}+k2\pi\\3x-\dfrac{\pi}{3}=\pi-\dfrac{\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{6}+\dfrac{k2\pi}{3}\\x=\dfrac{7\pi}{18}+\dfrac{k2\pi}{3}\end{matrix}\right.\)
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