Q. 15 B4.3( 6 Votes )

# prove that:

sin^{2}(n + 1)A – sin^{2}nA = sin(2n + 1)A sinA

Answer :

__We know that sin ^{2}A – sin^{2}B = sin(A +B) sin(A –B)__

HereA =(n + 1)A And B = nA

⇒ LHS: sin^{2}(n + 1)A – sin^{2}nA = 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.

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