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NDA 2025 · PYQ · Inverse Trigonometry · easy

If k is a root of x² - 4x + 1 = 0, then what is tan⁻¹k + tan⁻¹(1/k) equal to?

  1. A.-π/2
  2. B.0
  3. C.π/4
  4. D.π/2✓ Correct

Explanation

The roots of x² - 4x + 1 = 0 are 2±√3, both positive. For any k > 0, tan⁻¹k + tan⁻¹(1/k) = π/2.
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