smallest degree that satisfies 2cos^2x-3cosx=2

Answer 1

2cos^2x-3cosx=2
2cos^2x - 3cosx - 2 = 0
(2cosx + 1)(cosx - 2) = 0
cosx = -1/2 or cosx = 2, the last part is not possible

cosx = -1/2, so the smallest angle is in quadrant II
x = 120° or 2π/3 rads , assuming you wanted the smallest positive angle