求证:2sin(π/4+a)sin(π/4-a)=cos2a
问题描述:
求证:2sin(π/4+a)sin(π/4-a)=cos2a
答
证明:2sin(π/4+a)sin(π/4-a) =2(sinπ/4cosa+cosπ/4sina)(sinπ/4cosa-cosπ/4sina) =2*√2/2(cosa+sina)*√2/2*(cosa-sina) =cosa*cosa-sinasina =cos2a.