First, we apply compound angle formula on sin(x+60).
sin(x+60) = sin(x)cos(60) + sin(60)cos(x) = 1/2sin(x) + sqrt(3)/2cos(x)
We now have:
2sin(x) = 1/2sin(x) + sqrt(3)/2cos(x)
Since sin(x) is not equal to 0 (if sin(x) is equal to 0, it is not possible for sin(x+60) to be equal to 0 as well), we can divide both sides of the equation by sin(x).
2 = 1/2 + sqrt(3)/(2tan(x))
Making tan(x) the subject,
3/2 = sqrt(3)/(2tan(x))
tan(x) = 1/sqrt(3).
Therefore,
x = 30 + 360n
The 360n is because trigonometric functions are periodic about 360 degrees, or 2pi radians, which means the equation will still hold no matter how much you add or subtract 360 degrees from x.