Question

求函数y=2sinxcosx+sinx-cosx的值域

Answer 1

2sinxcosx=2sinxcosx-（sinx）^2-(cosx)^2+1=1-(sinx-cosx)^2

令sinx-cosx=t,则y=1-t^2+t=-(t-1/2)^2+5/4

t=sinx-cosx=根2sin(x-pi/4)

所以,根2≥t≥-根2

所以,5/4≥y≥-1-根2