答案:设1小于等于COSx-SINx小于等于根号2,则函数y=1-cos x+sin x+sinx cosx的值域为?

1≤cosa-sina≤√2 cosa-sina=√2 sin(π/4-x)∴√2 /2 ≤sin(π/4-x)≤1 ∴-π/2≤x≤0设m=cosa-sina 所以m^2=1-2sinxcosxsinxcosx=(1-m^2)/2y=1-m+(1-m^2)/2=-1/2(m^2+2m-3) 对称轴m=-11≤m≤√2所以 y在 1≤m≤√2单调递减(1-2√2)/2≤y≤0 既1/2-√2≤y≤0