Given that
#\cos(x-30^\circ)=2\cos(x+30^\circ)#
#\cosx\cos(30^\circ)+\sin x\sinx(30^\circ)=2(\cosx\cos(30^\circ)-\sin x\sinx(30^\circ))#
#\cos x\cdot \sqrt3/2+\sin x\cdot 1/2=2(\cos x\cdot \sqrt3/2-\sin x\cdot 1/2)#
#\sqrt3 \cos x+\sin x\=2\sqrt 3\cos x-2\sin x#
#\sin x+2\sin x=2\sqrt3\cos x-\sqrt3\cos x#
#3\sin x=\sqrt3\cos x#
#\frac{\sin x}{\cos x}=\sqrt3/3#
#\tan x=1/\sqrt3#
#\tan x=\tan(\pi/6)#
#x=k\pi +\pi/6#
Where #k# is any integer i.e. #k=0, \pm1, \pm2, \pm3, \ldots#
Since, #0 < x< \360^\circ# hence setting #k=0, 1#, we get desired values as follows
#x=30^\circ, 210^\circ#
