Solve 2cos^2x+sinx-1=0, if 0<=x<=2pi

x = π/2, 7π/6, 11π/6

Step-by-step explanation:

2 cos² x + sin x - 1 = 0

Use Pythagorean identity:

2 (1 - sin² x) + sin x - 1 = 0

2 - 2 sin² x + sin x - 1 = 0

-2 sin² x + sin x + 1 = 0

2 sin² x - sin x - 1 = 0

Factor:

(sin x - 1) (2 sin x + 1) = 0

Solve:

sin x = 1 or - 1/2

x = π/2, 7π/6, 11π/6