Find the exact solutions to each equation for the interval [0,360)

Question

2cosx-secx = 1

Answer 1

2 cosx - 1/cosx = 1
(2cos^2 x - 1)cosx = 1
2cos^2 x - 1 = cosx
2cos^2 x - cosx - 1 = 0
(2cosx + 1)(cosx-1) = 0
cosx = -1/2 or cosx = 1
x = 120º, 240º,0º,360º