first equation gives us sin 2x = (sqrt 3)/2 and we know that this is the value for sin pi/3

Also the trig ratio sine is positive in 1st and 2nd quadrant thus sin pi/3 = sin 2pi/3 = (sqrt 3 )/2

Hence we have 2x = pi/3 OR 2x= 2pi/3 that gives x = pi/6 or x = pi/3

Similarly proceed for other equations