Question

证明sin(x+y)sin(x-y)=（sinx）^2-(siny）^2.

Answer 1

解：sin(x+y)sin(x-y)
=-1/2(cos(x+y+x-y)—cos(x+y-x+y))
=-1/2(cos2x—cos2y)
=-1/2(1-2（sinx）^2-1+2(siny）^2)
=（sinx）^2-(siny）^2

Answer 2

左边=(sinxcosy+cosxsiny)(sinxcosy-cosxsiny)
=sin²xcos²y-cos²xsin²y
=sin²x(1-sin²y)-(1-sin²x)sin²y
=sin²x-sin²xsin²y-sin²y+sin²xsin²y
=sin²x-sin²y
=右边
命题得证