If tan⁻¹x + tan⁻¹y + tan⁻¹z = π/2, then xy + yz + zx equals:
If tan⁻¹x + tan⁻¹y + tan⁻¹z = π/2, then xy + yz + zx equals:
- A. 1
- B. 0
- C. −1
- D. 2
Answer: A) 1
Explanation: We know tan⁻¹x + tan⁻¹y + tan⁻¹z = tan⁻¹((x+y+z−xyz)/(1−xy−yz−zx)). For sum = π/2, denominator must be 0, so 1 − (xy+yz+zx) = 0 → xy+yz+zx = 1.
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