d.
\(\left(2sinx-4cosx+1\right)\left(1+sinx\right)=1-sin^2x\)
\(\Leftrightarrow\left(2sinx-4cosx+1\right)\left(1+sinx\right)=\left(1+sinx\right)\left(1-sinx\right)\)
\(\Leftrightarrow\left(1+sinx\right)\left(3sinx-4cosx\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}1+sinx=0\\3sinx=4cosx\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=-1\\tanx=\dfrac{4}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{2}+k2\pi\\x=arctan\left(\dfrac{4}{3}\right)+k\pi\end{matrix}\right.\)
e.
ĐKXĐ: \(sin2x\ne0\Rightarrow x\ne\dfrac{k\pi}{2}\)
\(\dfrac{sin3x.cos2x}{sin2x}=0\)
\(\Rightarrow\dfrac{\left(3sinx-4sin^3x\right)cos2x}{2sinx.cosx}=0\)
\(\Rightarrow\dfrac{\left(3-4sin^2x\right)cos2x}{2cosx}=0\)
\(\Rightarrow\left(1+2cos2x\right)cos2x=0\)
\(\Rightarrow\left[{}\begin{matrix}cos2x=-\dfrac{1}{2}\\cos2x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\pm\dfrac{\pi}{3}+k\pi\\x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}\end{matrix}\right.\)