sin(2n+1)AsinA=sin²(n+1)A-sin²nA . Prove this .
we have formula sin2a - sin2b =sin(a-b)sin(a+b)
therefore
sin2(n+1)A - sin2nA=sin[(n+1)A+nA].sin[(n+1)A-nA]
=sin(2n+1)A.sinA =RHS
hence proved
Prove that sin x+sin 3x+......+sin(2n−1)x=sin2nxsin x.