Question

2cos5xcos3x+2sin5xsin3x>sqrt3

Answer 1

$2\cos5x\cos3x+2\sin5x\sin3x > \sqrt{3}$

$2\cos(5x-3x) > \sqrt{3}$

$\cos2x > \dfrac{\sqrt{3}}{2}$

$-\dfrac{\pi}{6}+2\pi n < 2x < \dfrac{\pi}{6}+2\pi n$

$-\dfrac{\pi}{12}+\pi n < x < \dfrac{\pi}{12}+\pi n,~~{\rm when~} n \in \mathbb{Z}$