1: \(\Leftrightarrow6\cdot\dfrac{1-cos2x}{2}+\dfrac{m}{2}\cdot sin2x-\dfrac{1+cos2x}{2}=2+m\)
\(\Leftrightarrow3\left(1-cos2x\right)+\dfrac{1}{2}m\cdot sin2x-\dfrac{1}{2}-\dfrac{1}{2}cos2x=m+2\)
\(\Leftrightarrow3-3cos2x+\dfrac{1}{2}m\cdot sin2x-\dfrac{1}{2}-\dfrac{1}{2}\cdot cos2x=m+2\)
\(\Leftrightarrow sin2x\cdot\dfrac{1}{2}m-\dfrac{7}{2}\cdot cos2x=m+2-\dfrac{1}{2}m+\dfrac{1}{2}-3\)
\(\Leftrightarrow sin2x\cdot\dfrac{1}{2}m-\dfrac{7}{2}\cdot cos2x=\dfrac{1}{2}m-\dfrac{1}{2}\)
Để pt có nghiệm thì \(\left(\dfrac{1}{2}m\right)^2+\dfrac{49}{4}>=\left(\dfrac{1}{2}m-\dfrac{1}{2}\right)^2\)
\(\Leftrightarrow\dfrac{1}{4}m^2+\dfrac{49}{4}>=\dfrac{1}{4}m^2-\dfrac{1}{2}m+\dfrac{1}{4}\)
=>-1/2m+1/4<=49/4
=>-1/2m<=12
hay m>=-24
2: \(\Leftrightarrow m\cdot\dfrac{1-cos2x}{2}-\dfrac{3}{2}sin2x=m+1\)
\(\Leftrightarrow m-m\cdot cos2x-3sin2x=2m+2\)
\(\Leftrightarrow-3\cdot sin2x-m\cdot cos2x=2m+2-m=m+2\)
Để pt có nghiệm thì \(\left(-3\right)^2+\left(-m\right)^2>=\left(m+2\right)^2\)
\(\Leftrightarrow m^2+9-m^2-4m-4>=0\)
=>-4m+5>=0
=>-4m>=-5
hay m<=5/4
