Question

Sin^2(n+1)A-Sin^2nA=Sin(2n+1)ASinA

Answer 1

Step-by-step explanation:

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.