令t=sinx+cosx
则
t=√2sin(x+45°)∈[-√2,√2]
而sinxcosx
=[(sinx+cosx)^2-(sinx)^2-(cosx)^2]/2
=(t^2-1)/2
∴原式=t+(t^2-1)/2
=[(t+1)^2-2]/2
y∈[-1,(1+2√2)/2]