[tex]\cos^22x-\sin^22x=\dfrac{\sqrt3}{2}\\\\\cos(4x)=\dfrac{\sqrt3}{2}\iff4x=30^o\to x=7.5^o\\----------------------\\\cos^22x-\sin^22x=\dfrac{\sqrt3}{2}\\\\\cos(4x)=\dfrac{\sqrt3}{2}\iff4x=\dfrac{\pi}{6}+2k\pi\ or\ 4x=-\dfrac{\pi}{6}+2k\pi\\\\\boxed{x=\dfrac{\pi}{24}+\dfrac{k\pi}{2}\ or\ x=-\dfrac{\pi}{24}+\dfrac{k\pi}{2}\ for\ k\in\mathbb{Z}}[/tex]
