题目

2sin(x+π/4)sin(x-π/4)=?

提问时间：2021-01-27

答案

2sin(x+π/4)sin(x-π/4)
=2sin(x+π/4)sin[-π/2+(π/4+x)]
=-2sin(x+π/4)cos(π/4+x)
=-sin(2x+π/2)
=-cos2x
2sin(x+π/4)sin(x-π/4)
=2(sinxcosπ/4+cosxsinπ/4)(sinxcosπ/4-cosxsinπ/4)
=2*(√2/2)²(sinx+cosx)(sinx-cosx)
=sin²x-cos²x
=-(cos²x-sin²x)
=-cos2x