f(x)=a(2sin^2 x/2+sinx)+b在区间【0,pai】上的值域为【2,3】,
f(x)=a(1-cosx+sinx)+b=a根号2sin(x-π/4)+a+b ； x-π/4∈【-π/4,3π/4】
a>0时,a根号2+a+b=3,& b=2; a=根号2-1 ,b=2;
a