\(\Leftrightarrow\cos^22x-\sin^22x-\sqrt{3}\sin4x-1=0\)
\(\Leftrightarrow\cos^22x-\left(1-\cos^22x\right)-2\sqrt{3}\sin2x\cos2x-1=0\)
\(\Leftrightarrow2\cos^22x-2\sqrt{3}sin2x\cos2x-2=0\)
\(\Leftrightarrow\cos^22x-\sqrt{3}sin2x\cos2x=1\)
\(\Leftrightarrow\cos2x\left(\cos2x-\sqrt{3}sin2x\right)=1\)
\(\Leftrightarrow\left\{{}\begin{matrix}\cos2x=1\\\cos2x-\sqrt{3}\sin2x=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{k\sqcap}{2}\\\dfrac{1}{2}\cos2x-\dfrac{\sqrt{3}}{2}\sin2x=\dfrac{1}{2}\left(1\right)\end{matrix}\right.\)
(1) \(\Leftrightarrow\sin\dfrac{\sqcap}{6}\cos2x-\cos\dfrac{\sqcap}{6}\sin2x=\dfrac{1}{2}\)
\(\Leftrightarrow\sin\left(\dfrac{\sqcap}{6}-2x\right)=\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{\sqcap}{6}-2x=\dfrac{\sqcap}{6}+k2\sqcap\\\dfrac{\sqcap}{6}-2x=\dfrac{5\sqcap}{6}+k2\sqcap\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k\sqcap\\x=\dfrac{-\sqcap}{3}+k\sqcap\end{matrix}\right.\)
\(\Rightarrow S=\left\{{}\begin{matrix}\left[{}\begin{matrix}x=k\sqcap\\x=\dfrac{-\sqcap}{3}+k\sqcap\end{matrix}\right.\\x=\dfrac{k\sqcap}{2}\end{matrix}\right.\)
