If tan⁻¹x + tan⁻¹y = 4π/5, then cot⁻¹x + cot⁻¹y equals:
If tan⁻¹x + tan⁻¹y = 4π/5, then cot⁻¹x + cot⁻¹y equals:
- A. π/5
- B. 2π/5
- C. 3π/5
- D. π/10
Answer: A) π/5
Explanation: tan⁻¹x + cot⁻¹x = π/2 for each x. Adding: (tan⁻¹x+tan⁻¹y) + (cot⁻¹x+cot⁻¹y) = π/2+π/2 = π. So cot⁻¹x+cot⁻¹y = π − 4π/5 = π/5.
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