求证:cos(x-w)*cosx=[cos(2x-w)+cos(w)]/2

问题描述:

求证:cos(x-w)*cosx=[cos(2x-w)+cos(w)]/2

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