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Question

Prove:tan3Atan2AtanA=tanAtan2Atan3A.

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Solution

LHS=tan3Atan2AtanA=tan(2A+A)(tan2A+tanA)=tan2A+tanA1tan2AtanA(tan2A+tanA)
=(tan2A+tanA)×11+tan2AtanA1tan2AtanA=tan2A+tanA1tan2AtanA×tan2AtanA=tan3Atan2AtanA=RHS
Hence Proved

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