4.
\(\Leftrightarrow\left(1-cos^22x\right)-\left(\dfrac{1-cos2x}{2}\right)=\dfrac{1}{2}\)
\(\Leftrightarrow2cos^22x-cos2x=0\)
\(\Rightarrow\left[{}\begin{matrix}cos2x=0\\cos2x=\dfrac{1}{2}\end{matrix}\right.\)
5.
\(2sinx.cosx+2cosx-sinx-1=0\)
\(\Leftrightarrow2cosx\left(sinx+1\right)-\left(sinx+1\right)=0\)
\(\Leftrightarrow\left(2cosx-1\right)\left(sinx+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=\dfrac{1}{2}\\sinx=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{2}+k2\pi\\x=\pm\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\) (đáp án khác)
6.
Phương trình có nghiệm khi:
\(\Delta=9-8\left(m+1\right)\ge0\Rightarrow m\le\dfrac{1}{8}\)