The number of solutions of tan⁻¹(x−1) + tan⁻¹x + tan⁻¹(x+1) = tan⁻¹(3x) is:
The number of solutions of tan⁻¹(x−1) + tan⁻¹x + tan⁻¹(x+1) = tan⁻¹(3x) is:
- A. 0
- B. 1
- C. 2
- D. 3
Answer: D) 3
Explanation: Applying tan on both sides and using tan⁻¹ formula, we get (3x(x²−x+1))/(1−3x²) = 3x. Solving yields x = 0, x = 1/√2, x = −1/√2, all valid. So 3 solutions.
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