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NDA 2025 · PYQ · Inverse Trigonometry · easy

If tan⁻¹k + tan⁻¹(1/2) = π/4, then what is the value of k?

Answer

The correct answer is C: 1/3. tan⁻¹k = π/4 - tan⁻¹(1/2). Taking tan: k = (1 - 1/2)/(1 + 1·1/2) = (1/2)/(3/2) = 1/3.

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

Explanation

tan⁻¹k = π/4 - tan⁻¹(1/2). Taking tan: k = (1 - 1/2)/(1 + 1·1/2) = (1/2)/(3/2) = 1/3.
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