[tex]2\cos5x\cos3x+2\sin5x\sin3x > \sqrt{3}[/tex]

[tex]2\cos(5x-3x) > \sqrt{3}[/tex]

[tex]\cos2x > \dfrac{\sqrt{3}}{2}[/tex]

[tex]-\dfrac{\pi}{6}+2\pi n < 2x < \dfrac{\pi}{6}+2\pi n[/tex]

[tex]-\dfrac{\pi}{12}+\pi n < x < \dfrac{\pi}{12}+\pi n,~~{\rm when~} n \in \mathbb{Z}[/tex]