Ta có: \({\sin}^2x-{\cos}^2x=\cos 4x\)
\(\Leftrightarrow -\cos 2x=\cos 4x\)
\(\Leftrightarrow 2\cos 3x\cos x=0\)
\(\Leftrightarrow \left[ \begin{array}{l} \cos 3x = 0\\\cos x= 0\end{array} \right. \)
\(\Leftrightarrow \left[ \begin{array}{l} 3x = \dfrac{\pi}{2}+k\pi,k\in\mathbb{Z}\\x= \dfrac{\pi}{2}+k\pi,\in\mathbb{Z}\end{array} \right. \)
\(\Leftrightarrow \left[ \begin{array}{l} x = \dfrac{\pi}{6}+k\dfrac{\pi}{3},k\in\mathbb{Z}\\ x= \dfrac{\pi}{2}+k\pi,\in\mathbb{Z}\end{array} \right. \)
\(\Leftrightarrow x=\dfrac{\pi}{6}+k\dfrac{\pi}{3},k\in\mathbb{Z}\)
Vậy phương trình có nghiệm là \(x=\dfrac{\pi}{6}+k\dfrac{\pi}{3},k\in\mathbb{Z}\)
