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For all admissible angles A, the expression tan3A*tan2A*tanA is equal to:

1. tan3A - tan2A - tanA
2. tan3A + tan2A + tanA
3. tan3A - tan2A + tanA
4. tanA - tan2A - tan3A

Correct answer: tan3A - tan2A - tanA

Solution

Expanding tan3A = tan(2A + A) and rearranging yields the identity tan3A*tan2A*tanA = tan3A - tan2A - tanA.

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