cos 2x - sin x = 0 note: cos 2x = 1 - 2sin^2x
1 - 2sin^2x - sinx = 0 multiply through by -1
2sin^2x + sin x - 1 = 0 factor
(2sinx - 1) (sinx + 1) = 0 set each factor to 0
2sinx - 1 = 0 add 1 to both sides
2sinx = 1 divide both sides by 2
sinx = 1/2 and this happens at pi/6 and 5pi/6 on the requested interval
And
sin x + 1 = 0 subtract 1 from both sides
sin x = -1 this happens at 3pi/2, which is outside the requested interval