Question

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

• A. $5$
• B. $13$
• C. $15$
• D. $23$
• E. $25$

Answer 1

The correct option is C $15$

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

$=1+{\tan }^2\left({\tan }^{-1}3\right)+1+{\cot }^2\left({\cot }^{-1}2\right)=1+3^2+1+2^2=15$