Question

求证：cos(x-w)*cosx=[cos(2x-w)+cos(w)]/2

Answer 1

2x-w=x+(x-w),w=x-(x-w)

∴cos(2x-w)+cos(w)=cos[x+(x-w)]+cos[x-(x-w)]

=cosxcos(x-w)-sinxsin(x-w)+cosxcos(x-w)+sinxsin(x-w)

=2cosxcos(x-w)

∴cosxcos(x-w)=[cos(2x-w)+cos(w)]/2