Question

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

• A. 11
• B. 15
• C. $1+\sec ^2\left(\tan ^{-1} 3\right)$
• D. $2+\operatorname{cosec}^2\left(\cot ^{-1} 3\right)$

Answer 1

Answer: (A), (C)

$\Theta \tan ^2 \theta=\sec ^2 \theta-1 \text { and } \cot ^2 \theta=\operatorname{cosec}^2 \theta-1$
$\therefore \text { Given expression }=\sec ^2\left(\sec ^{-1} 2\right)-1+\operatorname{cosec}^2\left(\operatorname{cosec}^{-1} 3\right)-1 $
$=4-1+9-1=11 $