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
答
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