What is cot2(sec-1 2) + tan2 (cosec-1 3) equal to ?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 11/12
  2. 11/24
  3. 7/24
  4. 1/24

Answer (Detailed Solution Below)

Option 2 : 11/24
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Explanation:

Let I = cot2 (sec-1 2) + tan2(cosec-1 3)

⇒ I = cot2 (60°) + tan 2 (cot-1 \(\sqrt 9 -1 \)

⇒ I = \(\frac{1}{3} + tan^2( tan^{-1}\frac{1}{\sqrt8})\)

⇒ I = \(\frac{1}{3} + \frac{1}{8} = \frac{11}{24}\)

∴ Option (b) is correct

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