Đk:\(cosxe0\)
\(\left(1\right)\Leftrightarrow\left(2cos^2x-1\right)+cosx\left[2\left(\frac{1}{cos^2x}-1\right)-1\right]=2\)
\(\Leftrightarrow\left(2cos^2x-1\right)+cosx\left(\frac{2}{cos^2x}-3\right)=2\)
\(\Leftrightarrow2cos^3x-3cos^2x-3cosx+2=0\)
\(\Leftrightarrow\left(1+cosx\right)\left(2cos^2x-5cosx+2\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}cosx=-1\\cosx=2\left(loai\right)\\cosx=\frac{1}{2}\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=\left(2k+1\right)\pi\\x=\pm\frac{\pi}{3}+k2\pi\end{array}\right.\left(k\in Z\right)\)
