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Prove the identity: tan(A) + tan(60 deg + A) + tan(120 deg + A) = 3 tan(3A). Which statement is correct?

1. The identity is true for all admissible A
2. The identity is false
3. It holds only when A = 0
4. The right side should be tan(3A), not 3 tan(3A)

Correct answer: The identity is true for all admissible A

Solution

The tangents of A, 60+A, 120+A are the three roots of an equation in tan(3A); the sum of these roots equals 3 tan(3A), proving the identity.

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