\(\Leftrightarrow\left(sin^2x-cos^2x\right)\left(sin^2x+cos^2x\right)=cos3x\)
\(\Leftrightarrow sin^2x-cos^2x=cos3x\)
\(\Leftrightarrow-cos2x=cos3x\)
\(\Leftrightarrow cos3x=cos\left(\pi-2x\right)\)
\(\Rightarrow\left[{}\begin{matrix}3x=\pi-2x+k2\pi\\3x=2x-\pi+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{5}+\dfrac{k2\pi}{5}\\x=-\pi+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left(cos^2x-sin^2x\right)\left(cos^2x+sin^2x\right)=cos3x\)
\(\Leftrightarrow cos^2x-sin^2x=cos3x\)
\(\Leftrightarrow cos2x=cos3x\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=2x+k2\pi\\3x=-2\pi+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k2\pi\\x=\dfrac{k2\pi}{5}\end{matrix}\right.\)