If tan⁻¹(x − 1) + tan⁻¹x + tan⁻¹(x + 1) = tan⁻¹(3x), then x equals:

If tan⁻¹(x − 1) + tan⁻¹x + tan⁻¹(x + 1) = tan⁻¹(3x), then x equals:

• A. 0
• B. 1/2
• C. 1
• D. −1/2

Answer: B) 1/2

Explanation: Using formula for sum of three arctangents, or simplifying pairwise: tan⁻¹(x−1)+tan⁻¹x = tan⁻¹((2x−1)/(1−x(x−1))). Further addition and equating to tan⁻¹(3x) yields x = 0 or x = ±1/2. Checking domains, x = 1/2 satisfies the equation.