Solve: tan⁻¹2x + tan⁻¹3x = π/4. Then x equals:
Solve: tan⁻¹2x + tan⁻¹3x = π/4. Then x equals:
- A. 1/6 or −1
- B. 1/6 or 1
- C. −1/6 or 1
- D. 1/3 or −1
Answer: A) 1/6 or −1
Explanation: tan⁻¹2x + tan⁻¹3x = tan⁻¹((5x)/(1−6x²)) = π/4. So (5x)/(1−6x²) = 1 → 5x = 1−6x² → 6x²+5x−1=0 → (6x−1)(x+1)=0 → x=1/6 or x=−1. Check validity: for x=−1, tan⁻¹(−2)+tan⁻¹(−3) is negative, sum ≈ −π/2 not π/4. So x=−1 extraneous. Only x=1/6.
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