Question

solve. cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y) = sin(x+y)

Answer 1

cosAcosB-sinAsinB=cos(A-B)
so
cos(pi/4-x-(pi/4-y))=sin(x+y)
=cos(pi/4-x-pi/4+y)=sin(x+y)
cos(-x+y)=sin(x+y)
cos(x-y)=sin(x+y)
cosxcosy-sinxsiny=sinxcosy-cosxsiny
cosxcosy-sinxcosy=sinxsiny-cosxsiny
cosy(cosx-sinx)=siny(sinx-cosx)
cosy(cosx-sinx)-siny(sinx-cosx)=0
cosy(cosx-sinx)+siny(cosx-sinx)=0
(cosx-sinx)(cosy+siny)=0
cosx-sinx=0 or cosy+siny=0