Question

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

• A. $5$
• B. $10$
• C. $15$
• D. $20$

Answer 1

The correct option is C $15$

${\sec }^2\left({\tan }^{-1}2\right)+cose{c}^2\left(co{t}^{-1}3\right)$

$={\sec }^2\left({\theta }_1\right)+{\csc }^2\left({\theta }_2\right)$

$\sec {\theta }_1=\sqrt{5}$

$cosec{\theta }_2=\sqrt{10}$

$⟹$ ${\sec }^2\left({\tan }^{-1}2\right)+cose{c}^2\left(co{t}^{-1}3\right)$ $=5+10=15$.