Solve 2cos2𝑥+cos𝑥−1=0for all solutions in the interval [0,360°)

Answer 1

2cos2x + cosx - 1 = 0
2(2cos^2x-1) + cosx - 1 = 0
4cos^2x + cosx - 3 = 0
(4cosx-3)(cosx+1) = 0
cosx = 3/4 or -1
since cos41.4° = 3/4,
x = 41.4°, 180°, 360-41.4°