Answer:
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
