we know that
sin(A-B)=sin A cos B - cos A sin B
then
sin(x-45)=sin x cos 45 - cos x sin 45
sin(45)=cos(45)=(√2)/2
sin(x-45)=sin x *[(√2)/2] - cos x*[(√2)/2]-------> [(√2)/2]*[sinx-cosx]
y=sin(x-45)=[(√2)/2]*[sinx-cosx]
using a graph tool
see the attached figure
the answer is
y=[(√2)/2]*[sinx-cosx]
