因为 sin(x-π/4)=sin[π/2-(x+π/4)]=cos(x+π/4)
所以 f(x)=2sin(x+π/4)sin(x-π/4)+sin2x
=2sin(x+π/4)cos(x+π/4)+sin2x
=sin(2x+π/2)+sin2x
=cos2x+sin2x
=√2[(√2/2)sin2x+(√2/2)cos2x]
=√2sin(2x+π/4)
所以 最大值为√2
因为 sin(x-π/4)=sin[π/2-(x+π/4)]=cos(x+π/4)
所以 f(x)=2sin(x+π/4)sin(x-π/4)+sin2x
=2sin(x+π/4)cos(x+π/4)+sin2x
=sin(2x+π/2)+sin2x
=cos2x+sin2x
=√2[(√2/2)sin2x+(√2/2)cos2x]
=√2sin(2x+π/4)
所以 最大值为√2