y=cos2x-2cosx
=2cos^2 x-2cosx-1
=2(cos^2 x-cosx+1/4)-1-1/2
=2(cosx-1/2)^2-3/2
当cosx=1/2时有最小值y=-3/2
当cosx=-1时有最大值y=3
所以b=3 a=-3/2
4a+b^2
=4*(-3/2)+3^2
=-6+9=3