so for cos x = - cos (pi/6), first u need to use the unit circle to find the angles where cosine equals to -root 3/2. Then since cosine is a negative, it cannot be in quadrants 1 or 4 meaning that it has to be in quadrant 2 and 3. The angles that equal to -root 3/2 in these quadrants would be 5pi/6 and 7pi/6. so x should be these variables.
If im wrong, im so sorry im rlly bad at maths methods 🙁