y=sinx-sin(x+π/4)
=sinx-[sinxcos(π/4)+cosxsin(π/4)]
=sinx-[(√2/2)sinx +(√2/2)cosx]
=(1- √2/2)sinx -(√2/2)cosx
=√[(1-√2/2)²+(-√2/2)²]sin(x+a),其中,tana=-(√2/2)/(1-√2/2)
=√(2 -√2)sin(x+a)
当sin(x+a)=1时,y有最大值ymax=√(2-√2)
当sin(x+a)=-1时,y有最小值ymin=-√(2-√2)