Question

Sin^2(x+y)-sin^2(x-y)=sin2xsin2y

Answer 1

sin²(x+y) - sin²(x-y) = [sin(x+y) - sin(x-y)][sin(x+y) + sin(x-y)] =

=(sinxcosy+sinycosx -sinxcosy+sinycosx)(sinxcosy+sinycosx +

+sinxcosy-sinycosx) = 2sinycosx·2sinxcosy =(2sinxcosx)(2sinycosy) =

= sin2x ·sin2y

Answer 2

Din a ^2-b^2=(a-b)(a+b)
Sin^2(x+y)-sin^2(x-y)=[sin(x+y)+sin(x-y)][sin(x+y)-sin(x-y)]=(sinx*cosy+cosx*siny+sinx*cosy-cosx*siny)(sinx*cosy+cosx*siny-sinx*cosy+cosx*siny)=2(sinx*cosy)*2(cosx*siny)=4sinx*cosx*siny*cosy=sin2x*sin2y