若方程1-2(cos^2)x-sinx+a=0有实数解,则实数a的取值范围是

1-2cos^2x-sinx+a=0
1-2(1-sin^2x)-sinx+a=0
1-2+2sin^2x-sinx+a=0
sin^2x-1/2sinx+(a-1)/2=0
(sinx-1/4)^2=1/16-(a-1)/2=(9-8a)/16
-1 ≤ sinx ≤ 1
0 ≤ (sinx-1/4)^2 ≤ (-1-1/4)^2 = 25/16
∴0 ≤ (9-8a)/16 ≤ 25/16
0 ≤ 9-8a ≤ 25
9 ≤ -8a ≤ 16
-9 ≥ 8a ≥ -16
-2 ≤ a ≤ -9/8