证明sin(x+y)sin(x-y)=(sinx)^2-(siny)^2.
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证明sin(x+y)sin(x-y)=(sinx)^2-(siny)^2.
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
左边=(sinxcosy+cosxsiny)(sinxcosy-cosxsiny)
=sin²xcos²y-cos²xsin²y
=sin²x(1-sin²y)-(1-sin²x)sin²y
=sin²x-sin²xsin²y-sin²y+sin²xsin²y
=sin²x-sin²y
=右边
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