cos^2a-cos(a+60)cos(a-60)=cos^2a-（cosacos60-sinasin60)(cosacos60+sinasin60)=cos^2a-[(cosacos60)^2-(sinasin60)^2]=cos^2a-(1/4cos^2a-3/4sin^2a)=3/4(cos^2a+sin^2a)=3/4