函数y=sinxcosx-sinx-cosx的值域是＿＿＿＿?

y=sinxcosx-sinx-cosx
= (1/2)* [(sinx + cosx)^2 - (sinx)^2 - (cosx)^2] - (sinx + cosx)
= (1/2)* [ (sinx + cosx)^2 - 1] - (sinx + cosx)
= (1/2)* (sinx + cosx)^2 - (sinx + cosx) - 1/2
= (1/2) * [(sinx + cosx)^2 - 2(sinx + cosx) + 1 - 1] - 1/2
= (1/2) * [ (sinx + cosx -1)^2 -1] -1/2
= (1/2)* (sinx + cosx -1)^2 -1
其中
sinx + cosx
= √2*[(√2/2)*sinx + (√2/2)*cosx]
=√2 *(sinx * cos45 + cosx *sin45)
= √2 * sin(x+45)
∈[-√2,√2]
sinx + cosx -1 ∈ [-√2 -1 ,√2 -1]
(sinx + cosx -1)^2 ∈ [ 0,3 + 2√2]
原式 ∈ (1/2)* [ 0,3 + 2√2] -1
= [-1,(1+2√2)/2]