2sin(x-π/4)sin(x+π/4)=?答案是-cos2x 还是cos2x

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2sin(x-π/4)sin(x+π/4)=?答案是-cos2x 还是cos2x

2sin(x-π/4)sin(x+π/4)=?答案是-cos2x 还是cos2x
2sin(x-π/4)sin(x+π/4)=?答案是-cos2x 还是cos2x

2sin(x-π/4)sin(x+π/4)=?答案是-cos2x 还是cos2x
2sin(x-π/4)sin(x+π/4)
=2(sinxcosπ/4-cosxsinπ/4)(sinxcosπ/4+cosxsinπ/4)
=2*√2/2*√2/2*(sinx+cosx)(sinx-cosx)
=sin²-cos²x
=-cos2x

2sin(x-π/4)sin(x+π/4)
= cos[(x-π/4)-(x+π/4)] - cos [(x-π/4)+(x+π/4)] ...【积化和差公式】
= cos(-π/2) - cos (2x)
= 0 - cos(2x)
= - cos(2x)