I really don't know where I'm going wrong, I use the sum to product formula but always end up far from sin(2x)sin(2y). Any help is appreciated, thanks.
Answer
(sin(x+y))2−(sin(x−y))2=(sinxcosy+cosxsiny)2−(sinxcosy+cosxsiny)2=(sin2cos2y+2sinxcosycosxsiny+cos2xsin2y)=−(sin2cos2y−2sinxcosycosxsiny+cos2xsin2y)=4sinxcosycosxsiny=(2sinxcosx)(2sinycosy)=sin(2x)sin(2y).
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