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Question

Prove that:
(i) cos245sin215=34
(ii) Sin2(n+1)Asin2nA=sin(2n+1)AsinA


Solution

(i) cos245sin215=34
(12)2sin215
=12(1cos2×152)
=12(1cos302)
=11+cos302
=cos302
=31×12=34
=RHS
LHS=RHS
Hence proved.
(ii) LHS: sin2(n+1)Asin2nA
=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)AsinA
=RHS
LHS=RHS
Hence proved.

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