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Answer:
sin2(n+1)A - sin2nA = sin(2n+1)A.sinA
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
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