Question

cos(2t) = sqrt(3)/2, 0 ≤ t ≤ 2π

Answer 1

Following that interval, we know that usually cos(x)= sqrt(3)/2 on: pi/6, and 11pi/6.
So WHAT has changed? Merely that we are multiplying by 2. Hmmm, but if we do this, with pi/6, it will result in pi/3, which is 1/2.
Simple solution: divide the original intervals that would give us the answer, by 2, to counter-act the 2 accompanying "x".
Thereby, your answers would be pi/6, and 11pi/12.
I hope this helped, feel free to pst me if you require assistance with this, or anything else. :)