Find all solutions of the equation in 0 2 2 cos 2 x sinx 1

Find all solutions of the equation in [0, 2). 2 cos ^2 \\(x\\) + sin(x) = 1

Solution

2cos^2x+sinx=1 for 0 < x < 360 deg
2(1-sin^2x)+sinx=1
2-2sin^2x+sinx=1
-2sin^2x+sinx+1=0
2sin^2x-sinx-1=0
(2sinx+1)(sinx-1)=0
..

2sinx+1=0
sinx=-1/2
x=210º and 330º (in quadrants III and IV where sin<0)
..
sinx-1=0
sinx=1
x=90º
..
ans:
x=210º, 330º and 90º