sin2x+sin2y=2sin(x+y)cos(x-y) 怎么算?

Question

如题所述

Answer 1

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