\(\Leftrightarrow2sin^2x-\left(2m-2\right)\cdot sin2x-\left(2m-2\right)\cdot cos^2x=2m\)
\(\Leftrightarrow1-cos2x-\left(2m-2\right)\cdot sin2x-\left(m-1\right)\cdot\left(1+cos2x\right)=2m\)
\(\Leftrightarrow1-cos2x-\left(2m-2\right)\cdot sin2x-m+1-cos2x\left(m-1\right)=2m\)
\(\Leftrightarrow\left(-2m+2\right)sin2x+cos2x\left(-m+1-1\right)-m+2=2m\)
=>(-2m+2)sin2x+cos2x(-m)=2m+m-2=3m-2
Để phương trình có nghiệm thì \(4m^2-8m+4+m^2>=9m^2-12m+4\)
=>9m^2-12m+4<=5m^2-8m+4
=>4m^2-4m<=0
=>m(m-1)<=0
=>0<=m<=1
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