1-2cos^2x-sinx+a=01-2(1-sin^2x)-sinx+a=01-2+2sin^2x-sinx+a=0sin^2x-1/2sinx+(a-1)/2=0(sinx-1/4)^2=1/16-(a-1)/2=(9-8a)/16-1 ≤ sinx ≤ 10 ≤ (sinx-1/4)^2 ≤ (-1-1/4)^2 = 25/16∴0 ≤ (9-8a)/16 ≤ 25/160 ...