sin2x+sin2y=2sin(x+y)cos(x-y) 怎么算?
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2sin(x+y)cos(x-y)
=2(sinxcosy+cosxsiny)(cosxcosy+sinxsiny)
=2sinxcosxcos²y+2sinycosysin²x+2sinycosycos²x+2sinxcosxsin²y
=sin2xcos²y+sin2ysin²x+sin2ycos²x+sin2xsin²y
=sin2x(sin²y+cos²y)+sin2y(sin²x+cos²x)
=sin2x+sin2y
=2(sinxcosy+cosxsiny)(cosxcosy+sinxsiny)
=2sinxcosxcos²y+2sinycosysin²x+2sinycosycos²x+2sinxcosxsin²y
=sin2xcos²y+sin2ysin²x+sin2ycos²x+sin2xsin²y
=sin2x(sin²y+cos²y)+sin2y(sin²x+cos²x)
=sin2x+sin2y
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