Question

The value of $\tan^2(\sec^{-1}2)+\cot^2(cosec^{-1}3)$ is

• A. 13
• B. 15
• C. 11
• D. none of these.

Answer 1

Answer: (C)

11

Answer 2

$tan^{2} \left(sec^{-1}2 \right) = sec^{2}\left(sec^{-1} 2\right) -1$ $cot^{2}\left(cosec^{-1} 3\right) = cosec^{2} \left(cosec^{-1} 3\right)-1$ $\therefore$ given expression $= \left(sec \left(sec^{-1}2\right)\right)^{2} + \left(cosec\left(cosec^{-1}3\right)\right)^{2} - 2$ $= \left(2\right)^{2} +\left(3\right)^{2}-2 = 11$