4 cos 2x + 3 cos x = 1

1 answer

recall that cos 2x = 2cos^2 x - 1

4 cos 2x + 3 cos x = 1
4(2cos^2 x - 1) + 3cosx - 1 = 0
8cos^2 x - 4 + 3cosx - 1 = 0
8cos^2 x + 3cosx - 5 = 0
(cosx + 1)(8cosx - 5) = 0
cosx = -1 or cosx = 5/8
x = 180° or x = 51.32° or x = 308.68°

or, in radians

x = π, or x = .8957 or x = 5.388