f(x)=sin(x-π/4)+cos(x-3π/4)
=sinxcos(π/4)-cosxsin(π/4)+cosxcos(3π/4)+sinxsin(3π/4)
=√2/2(sinx-cosx-cosx+sinx)
=√2（sinx-cosx）
=2（√2/2*sinx-√2/2cosx）
=2sin(x-π/4)