\(\Leftrightarrow m\cdot\dfrac{1-cos4x}{2}+cos4x=m\)
\(\Leftrightarrow m\cdot\left(\dfrac{1}{2}-\dfrac{1}{2}cos4x\right)+cos4x=m\)
\(\Leftrightarrow-m\cdot\dfrac{1}{2}\cdot cos4x+cos4x=m-\dfrac{1}{2}m=\dfrac{1}{2}m\)
\(\Leftrightarrow cos4x\left(-\dfrac{1}{2}m+1\right)=\dfrac{1}{2}m\)
Để pt có nghiệm thì \(-1< =\dfrac{1}{2}m:\left(\dfrac{-m+2}{2}\right)< =1\)
\(\Leftrightarrow-2< =m\cdot\dfrac{2}{2-m}< 2\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2m}{2-m}+2>=0\\\dfrac{2m}{2-m}-2< =0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2m+4-2m}{2-m}>=0\\\dfrac{2m-4+2m}{2-m}< =0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2-m>0\\\dfrac{4m-4}{m-2}>=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m< 2\\\left[{}\begin{matrix}m>2\\m< =1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow m< =1\)
