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If x, y, z are in arithmetic progression and arctan(x), arctan(y), arctan(z) are also in arithmetic progression, then which relation must hold?

1. x = y = z
2. 2x = 3y = 6z
3. 6x = 3y = 2z
4. 6x = 4y = 3z

Correct answer: x = y = z

Solution

From the arctan AP, 2*arctan y = arctan x + arctan z. Using x + z = 2y and the addition formula leads to a relation that is only consistent when all three are equal.

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