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Evaluate the expression: tan( tan⁻¹x + tan⁻¹y + tan⁻¹z) − cot( cot⁻¹x + cot⁻¹y + cot⁻¹z).

1. 0
2. 2(x + y + z)
3. 3π/2
4. 3π/2 + x + y + z

Correct answer: 0

Solution

Let S = tan^-1 x + tan^-1 y + tan^-1 z. Then cot^-1 x + cot^-1 y + cot^-1 z = 3pi/2 - S, and cot(3pi/2 - S) = tan S. So the expression is tan S - tan S = 0.

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