2sin2x+cosx-1=0

Answer 1

2sin²x + cosx - 1 = 0

2(1 - cos²x) + cosx - 1 = 0

-2cos²x + cosx + 1 = 0

2cos²x - cosx - 1 = 0

(2cosx + 1)(cosx - 1) = 0

cosx = -1/2 or cosx = 1

cosx = -1/2 when x = 2π/3 or 4π/3

cosx = 1 when x = 0 or 2π

Note: the solutions listed are the solutions in the interval [0, 2π]. To get other solutions, add any multiple of 2π to the listed values.