Question

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

• A. $13$
• B. $15$
• C. $11$
• D. None of these

Answer 1

The correct option is C $11$

${\tan }^2\left(se{c}^{-1}\right(2\left)\right)+{\cot }^2\left(cose{c}^{-1}\right(3\left)\right)$
$={\sec }^2\left(se{c}^{-1}\right(2\left)\right)-1+cose{c}^2\left(cose{c}^{-1}\right(3\left)\right)-1$
$=2^2-1+3^2-1$
$=4+9-2$
$=13-2$
$=11$