=cos(π/4)sin[a+(π/4)]-sin[(π/2)-{a+(π/4)}]sin(π/4)
=cos(π/4)sin[a+(π/4)]-cos[a+(π/4)]sin(π/4)
=sin[a+(π/4)]cos(π/4)-sin(π/4)cos[a+(π/4)]
=sin{[a+(π/4)]-(π/4)}
=sina
=cos(π/4)sin[a+(π/4)]-sin[(π/2)-{a+(π/4)}]sin(π/4)
=cos(π/4)sin[a+(π/4)]-cos[a+(π/4)]sin(π/4)
=sin[a+(π/4)]cos(π/4)-sin(π/4)cos[a+(π/4)]
=sin{[a+(π/4)]-(π/4)}
=sina