Wednesday, 27 August 2014

algebra precalculus - How do I show sin2(x+y)sin2(xy)sin(2x)sin(2y)?



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(xy))2=(sinxcosy+cosxsiny)2(sinxcosy+cosxsiny)2=(sin2cos2y+2sinxcosycosxsiny+cos2xsin2y)=(sin2cos2y2sinxcosycosxsiny+cos2xsin2y)=4sinxcosycosxsiny=(2sinxcosx)(2sinycosy)=sin(2x)sin(2y).


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