May i ask how you did the last line? I thought that second quadrant was 180-alpha, but it says 2pi /3 which is 120, and alpha is 30? Sorry and thank you

The tutor is correct, but could have explained slightly better (and I almost mistook the sin 2x and the cos 2x as sin^2 x and cos^2 x in one of the lines).

For this question, the angle which is subject to the A-S-T-C quadrant is 2x, not x, because we are solving for the equation Tan 2x = sqrt 3.

As such, the angle 2x MUST lie in the first or the third quadrants. Note, however, that the angle x does not necessarily have to be in the first or third quadrants, because the condition is only applicable for the angle in which we took the inverse tangent (the 2x).

However, of course the values of x depend on the values of 2x which we have obtained.

Thank you! I got it

If a question is like, say

cos (2x - 30) = 0.5,

then the angle 2x - 30 is subject to the respective valid quadrants, but the angle x does not necessarily have to be in a specific quadrant.

Thanks for the clarification, I was thinking about it for an hour before this