\(\Leftrightarrow\left(sin^2x+cos^2x\right)^3-3sin^2x.cos^2x\left(sin^2x+cos^2x\right)+\frac{3}{2}sin2x-m+2=0\)
\(\Leftrightarrow1-3sin^2x.cos^2x+\frac{3}{2}sin2x-m+2=0\)
\(\Leftrightarrow1-\frac{3}{4}sin^22x+\frac{3}{2}sin2x-m+2=0\)
\(\Leftrightarrow-\frac{3}{4}sin^22x+\frac{3}{2}sin2x+3=m\)
Đặt \(sin2x=t\Rightarrow t\in\left[-1;1\right]\)
\(\Rightarrow-\frac{3}{4}t^2+\frac{3}{2}t+3=m\)
Xét \(f\left(t\right)=-\frac{3}{4}t^2+\frac{3}{2}t+3\) trên \(\left[-1;1\right]\)
\(-\frac{b}{2a}=1\) ; \(f\left(-1\right)=\frac{3}{4}\) ; \(f\left(1\right)=\frac{15}{4}\)
\(\Rightarrow\frac{3}{4}\le f\left(t\right)\le\frac{15}{4}\Rightarrow\frac{3}{4}\le m\le\frac{15}{4}\)
