1) 2cos^2x - 1 - sinx = 0 2) 2sin^2x - 1 + cosx = 0 3) 2cos^2x - 1 + sinx = 0 4) cos2x - cosx = 0 5) sinx + cosx + sin3x = 0 6) 2sin^2x - 5sinxcosx + 5cos^2x = 1 7) sqrt3cosx - sinx = 0 8) sqrt3cosx - sinx = 1 9) sin^2x + cos^2 2x + sin^2 3x = 3/2

(1)
2 cos²x = 1 + sin x
2 - 2 sin²x = 1 + sin x
2 sin²2 + sin x - 1 = 0
D = 1 + 8 = 3²
sin x = (1 + 3) / 4 = 1
sin x = (1 - 3) / 4 = - 1/2