y=sinxcosx/sinx+cosx+1的值域?

设sinx+cosx=t ,sinx+cosx=√2sin(x+π/4)
所以t属于[-√2,√2]
t^2=1+2sinxcosx , sinxcosx=(t^2-1)/2
f(x）=（t^2-1）/[2(1+t)]=(t-1)/2属于[-(√2+1)/2,(√2-1)/2]
另外,分母不为零,所以1+sinx+cosx≠0 ,即t≠-1
综上,值域是[-(√2+1)/2,-1）∪（-1,(√2-1)/2]