First slide

Properties of ITF

Question

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

Moderate

A

5
B

10
C

11
D

15

Solution

$\tan^{2} (\sec^{- 1} 2) + \cot^{2} ({cosec}^{- 1} 3)$
$= \sec^{2} (\sec^{- 1} 2) - 1 + {cosec}^{2} ({cosec}^{- 1} 3) - 1$
$\begin{array}{l} = {\{\sec (\sec^{- 1} 2)\}}^{2} - 1 + {\{cosec ({cosec}^{- 1} 3)\}}^{2} - 1 \\ = 2^{2} - 1 + 3^{2} - 1 = 11 \end{array}$

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