Question

$\sec^2(\tan^{-1}2)+cosec^2(\cot^{-1}3)=$

• A. 5
• B. 10
• C. 15
• D. 20

Answer 1

Answer: (C)

15

Answer 2

$sec^{2}\left(tan^{-1}2\right) = 1 +tan^{2}\left(tan^{-1}2\right)$ $= 1+\left(2\right)^{2} = 5$ $cosec^{2}\left(cot^{-1} 3\right) = 1+ cot^{2} \left(cot^{-1} 3\right)$ $= 1+\left(3\right)^{2} = 10$ $\therefore$ reqd. value $= 5+10$ $= 15$