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NDA 2 2024 Maths, question 22

Topic: Trigonometry

Q22

What is cot⁡2(sec⁡−12)+tan⁡2(cosec⁡−13)\cot ^{2}(\sec ^{-1}2)+\tan ^{2}(\operatorname{cosec} ^{-1}3) equal to?

  1. (a) 11/1211/12
  2. (b) 11/2411/24Correct answer
  3. (c) 7/247/24
  4. (d) 1/241/24

Solution.

Answer: (b) 11/2411/24

  1. If sec u=2, then tan²u=3 and cot²u=1/3.
  2. If cosec v=3, then cot²v=8 and tan²v=1/8.
  3. The required sum is 1/3+1/8=11/24.