求证cos(a+b)cos(a－b)=cos^2b－sin^2a
问题描述：
求证cos(a+b)cos(a－b)=cos^2b－sin^2a
答
cos(a+b)cos(a－b)=(cosacosb-sinasinb)(cosacosb+sinasinb)=(cosacosb)^2-(sinasinb)^2=cos^2acos^2b-sin^2asin^2b=cos^2acos^2b-(1-cos^2a)(1-cos^2b)=cos^2acos^2b-(1-cos^2a-cos^2b+cos^2acos^2b)=cos^2acos^2b-...