Prove that, sin2x+sin2y=2sin(x+y)cos(x-y).
help please
Thanks in advance.
sin(x+y) = sinx*cosy + cosx*siny
cos(x-y) = cosx*cosy + sinx*siny
sin(x+y)*cos(x-y) = sinxcosy*cosxcosy + sinxcosy*sinxsiny + cosxsiny*cosxcosy + cosxsiny*sinxsiny
= sinxcosx*cos^2y + sinycosy*sin^2x + sinycosy*cos^2x + sinxcosx*sin^2y
So
2sin(x+y)cos(x-y) = 2[sinxcosx(sin^2y + cos^2y) + sinycosy(sin^2x + sin^2y)]
= 2sinxcosx + 2sinycosy
= sin2x + sin2y