证明2sin(π/4+x)sin(π/4-x)=cos2x
问题描述：
证明2sin(π/4+x)sin(π/4-x)=cos2x
答
2sin(π/4-x)sin(π/4+x)
=2(sinπ/4cosx-cosπ/4sinx)(sinπ/4cosx+cosπ/4sinx)
=2[(sinπ/4cosx)^2-(cosπ/4sinx)^2]
=2[(cosx)^2/2-(sinx)^2/2]
=(cosx)^2-(sinx)^2
=cos2x