\(\Leftrightarrow3sinx-3sin^3x-4cos^3x=0\)
\(\Leftrightarrow3sinx\left(1-sin^2x\right)-4cos^3x=0\)
\(\Leftrightarrow3sinx.cos^2x-4cos^3x=0\)
\(\Leftrightarrow cos^2x\left(3sinx-4cosx\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos^2x=0\\3sinx=4cosx\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\tanx=\frac{4}{3}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{2}+k\pi\\x=arctan\left(\frac{4}{3}\right)+k\pi\end{matrix}\right.\)
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