Question

The value of ${\sin }^{-1}(\sin 9)+{\tan }^{-1}(\tan 9)+{\sec }^2\left({\tan }^{-1}2\right)+{\mathrm{cosec}}^2\left({\cot }^{-1}3\right)$ is equal to

• A. $6\pi -3$
• B. $6\pi -5$
• C. 13
• D. 15

Answer 1

Answer: (D)

${\sin }^{-1}(\sin 9)+{\tan }^{-1}(\tan 9)+{\sec }^2\left({\tan }^{-1}2\right)+{\mathrm{cosec}}^2\left({\cot }^{-1}3\right)$
$=(3\pi -9)+(9-3\pi )+5+10=15$