ĐKXĐ: \(x\ne\frac{\pi}{6}+\frac{k\pi}{3}\)
\(\Leftrightarrow\frac{cos^2x-cos3x.cos5x}{cos3x.cosx}-4\left[1-2sin^2\left(2x+\frac{11\pi}{2}\right)\right]-4cos2x=0\)
\(\Leftrightarrow\frac{2cos^2x-cos2x-cos8x}{cos4x+cos2x}-4cos\left(4x+11\pi\right)-4cos2x=0\)
\(\Leftrightarrow\frac{1-cos8x}{cos4x+cos2x}+4cos4x-4cos2x=0\)
\(\Leftrightarrow1-cos8x+4\left(cos4x-cos2x\right)\left(cos4x+cos2x\right)=0\)
\(\Leftrightarrow1-cos8x+4cos^24x-4cos^22x=0\)
\(\Leftrightarrow1-\left(2cos^24x-1\right)+4cos^24x-2\left(1+cos4x\right)=0\)
\(\Leftrightarrow cos^24x-cos4x=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos4x=0\\cos4x=1\end{matrix}\right.\) \(\Leftrightarrow...\)
