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NDA 2 2025 Maths, question 50

Topic: Trigonometry

Q50

What is the value of tan⁡[12sec⁡−1(23)]\tan \left\lbrack \frac{1}{2}\sec ^{-1}(\frac{2}{\sqrt{3}}) \right]?

  1. (a) 2−32-\sqrt{3}Correct answer
  2. (b) 2+32+\sqrt{3}
  3. (c) 3−1\sqrt{3}-1
  4. (d) 3+1\sqrt{3}+1

Solution.

Answer: (a) 2−32-\sqrt{3}

  1. The positive principal angle sec⁻¹(2/√3) is π/6.
  2. Half of it is π/12=15°, and tan15°=(√3−1)/(√3+1)=2−√3.