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Prove that (2 cos 2A + 1) / (2 cos 2A - 1) = tan(60 deg + A) * tan(60 deg - A). (Select the statement that correctly establishes the identity.)

1. True: both sides equal (2 cos 2A + 1)/(2 cos 2A - 1)
2. False: the right side equals its reciprocal
3. True only when A = 0
4. Identity holds only for A = 30 deg

Correct answer: True: both sides equal (2 cos 2A + 1)/(2 cos 2A - 1)

Solution

Expressing tan(60+A) tan(60-A) as a ratio of cosines and using 2 cos 2A + 1 = 4(cos² A - sin²(...)) shows both sides are equal, so the identity is true.

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