Question

${\tan }^2\left({\sec }^{-1}3\right)+{\text{cosec}}^2\left({\cot }^{-1}2\right)+{\cos }^2\left({\cos }^{-1}\frac{2}{3}+{\sin }^{-1}\frac{2}{3}\right)=$ _________.

• A. 15
• B. 16
• C. 14
• D. 13

Answer 1

Answer: (D)

${\tan }^2\left({\sec }^{-1}3\right)+{\text{cosec}}^2\left({\cot }^{-1}2\right)+{\cos }^2\left({\cos }^{-1}\frac{2}{3}+{\sin }^{-1}\frac{2}{3}\right)$
$={\tan }^2\left({\tan }^{-1}(2\sqrt{2})\right)+{\text{cosec}}^2\left({\text{cosec}}^{-1}\sqrt{5}\right)+{\cos }^2\left(\frac{\pi }{2}\right)$
$=8+5=13$