Answer
(a) $g(x)=2sin2(x+\frac{\pi}{12})$
(b) see graph.
Work Step by Step
(a) $g(x)=cos(2x)+\sqrt 3 sin(2x)=2(\frac{\sqrt 3}{2}sin(2x)+\frac{1}{2}cos(2x))
=2(sin(2x)cos(\frac{\pi}{6})+cos(2x)sin(\frac{\pi}{6}))$
Thus $g(x)=2sin(2x+\frac{\pi}{6})=2sin2(x+\frac{\pi}{12})$
(b) see graph.
