\(4cosx-3sin2x=0\)
\(\Leftrightarrow4cosx-6sinx.cosx=0\)
\(\Leftrightarrow2cosx\left(2-3sinx\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\sinx=\dfrac{2}{3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\x=arcsin\left(\dfrac{2}{3}\right)+k2\pi\\x=\pi-arcsin\left(\dfrac{2}{3}\right)+k2\pi\end{matrix}\right.\)