1/2 sinx - (rad3)/2 Cosx =1/2 Use trig ratios of standard angles and it is easy to guess that 1/2 = Cos 60deg and rad3/2 = Sin 60deg.So our equation is now

Cos60Sinx -Sin60Cosx = 1/2 this can be written as Sin(x-60) = 1/2.

One solution to the above equation will be 30deg.(In radian form,60deg = Pi/3 and 30deg is Pi/6)

So the General solution of the given equation is

x-pi/3=nPi + (-1)^nPi/6 or x = nPi + (-1)^nPi/6 + Pi/3 for all values of n belonging to Z,the set of integers.