2sina(x-π/4)sin(x+π/4) 怎么转换成(sinx-cosx)(sinx+cosx)?

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2sina(x-π/4)sin(x+π/4) 怎么转换成(sinx-cosx)(sinx+cosx)?
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2sina(x-π/4)sin(x+π/4) 怎么转换成(sinx-cosx)(sinx+cosx)?
2sina(x-π/4)sin(x+π/4) 怎么转换成(sinx-cosx)(sinx+cosx)?

2sina(x-π/4)sin(x+π/4) 怎么转换成(sinx-cosx)(sinx+cosx)?
2sin(x-π/4)sin(x+π/4)=sin(2x-π/2)=-cos2x
=-(cosx^2-sinx^2)=sinx^2-cosx^2=(sinx-cosx)(sinx+cosx)

由积化和差公式sina*sinb=-(cos(a+b)-cos(a-b))/2

-[cos2x-cos(π/2)]=-cos2x=-(cos²x-sin²x)=(sinx-cosx)(sinx+cosx)