d. pi/3 , 5 pi/3 , pi
Use the identity:
sin^2 x + cos^2 x = 1
Solve the quadratic by factoring and completing the square:
2sin^2 x + cos x = 2 (1 - cos^2 x ) - cos x
= -2 cos ^ x - cos x +2
= 1
2 cos^2 x+ cos x -1 = 0
(2 cosx-1 ) (cosx + 1 ) =0
SO:
cos x = 1/2 or cos x =-1
Cos x is positive for 0
x= pi/3 , or pi ,or 5/3 pi