Question

The value of
$\sin \left({\sin }^{-1}\frac{1}{3}+{\sec }^{-1}3\right)+$
$\cos \left({\tan }^{-1}\frac{1}{2}+{\tan }^{-1}2\right)$ is :

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A)

${\sin }^{-1}x+{\cos }^{-1}x=\frac{\pi }{2}$
and ${\tan }^{-1}x+{\cot }^{-1}x=\frac{\pi }{2}$
$\sin \left({\sin }^{-1}\frac{1}{3}+{\sec }^{-1}3\right)$
$+\cos \left({\tan }^{-1}\frac{1}{2}+{\tan }^{-1}2\right)$
$=\sin \left({\sin }^{-1}\frac{1}{3}+{\cos }^{-1}\frac{1}{3}\right)$
$+\cos \left({\tan }^{-1}\frac{1}{2}+{\cot }^{-1}\frac{1}{2}\right)$
$=\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)=1$