prove that:
sin2(n + 1)A – sin2nA = sin(2n + 1)A sinA
We know that sin2A – sin2B = sin(A +B) sin(A –B)
HereA =(n + 1)A And B = nA
⇒ LHS: sin2(n + 1)A – sin2nA = sin((n + 1)A + nA) sin((n + 1)A – nA)
= sin(nA +A + nA) sin(nA +A – nA)
= sin(2nA +A) sin(A)
= sin(2n + 1)A sinA = RHS
Hence proved.