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NDA 1 2025 Maths, question 50

Topic: Trigonometry

Q50

If tan⁡−1k+tan⁡−1(1/2)=π/4\tan^{- 1}k + \tan^{- 1}(1/2) = \pi/4, then what is the value of kk?

  1. (a) 11
  2. (b) 1/21/2
  3. (c) 1/31/3Correct answer
  4. (d) 1/41/4

Solution.

Answer: (c) 1/31/3

  1. Take the tangent of tan⁡−1k=π/4−tan⁡−1(1/2)\tan^{- 1}k = \pi/4 - \tan^{- 1}(1/2).
  2. Then k=(1−1/2)/(1+1/2)=1/3k = (1 - 1/2)/(1 + 1/2) = 1/3.