CUET · MATHS · PYQ PAPER 2025
The value of \(\tan ^2\left(\sec ^{-1} 2\right)+\cot ^2\left(\operatorname{cosec}^{-1} 3\right)\) in equal to
- A 6
- B 11
- C 13
- D 15
Answer & Solution
Correct Answer
(B) 11
Step-by-step Solution
Detailed explanation
\(\tan ^2\left(\sec ^{-1} 2\right) = \left(\sec\left(\sec ^{-1} 2\right)\right)^2 - 1 = 2^2 - 1 = 3\) \(\cot ^2\left(\operatorname{cosec}^{-1} 3\right) = \left(\operatorname{cosec}\left(\operatorname{cosec}^{-1} 3\right)\right)^2 - 1 = 3^2 - 1 = 8\) \(3 + 8 = 11\)
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