Question

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

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

Answer 1

Answer: (A), (C)

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