(1). b=-2时，f(x)=(sinx)^2+a(sinx)+(a^2-3)/a
g(y)=y^2+ay+(a^2-3)/a
对任意x，-1<=sinx<=1，若f(x)<0
即：-1<=y<=1时，g(y)<0
==> g(-1)<0,g(1)<0
1-a+(a^2-3)/a<0, 1+a+(a^2-3)/a<0
==> 0<a<1
(2). g(y)=y^2+ay+(a^2-3)/a
g(y)取最小值时，y=-a/2，-1<=-a/2<=1 ...(1)
并且，g(y)最小值 =(a^2+b-1)/a <=0 ...(2)
a>=2, (1)(2)==> a=2,b<=-3
a^2+b^2-8a =b^2-12 <= (-3)^2-12 =-3
即：a=2，b=-3时，a^2+b^2-8a取最小值-3
