Question

The value of $\sin ({\sin }^{-1}\frac{1}{x}+{\sec }^{-1}x),|x|\ge 1$ is

$\left(a\right)1\left(b\right)-1\left(c\right)0\left(d\right)\frac{1}{2}$

Answer 1

$\sin ({\sin }^{-1}\frac{1}{x}+{\sec }^{-1}x)$
$=\sin ({\sin }^{-1}\frac{1}{x}+{\cos }^{-1}\frac{1}{x})(\because {\sec }^{-1}x={\cos }^{-1}\frac{1}{x})$
$=\sin \frac{\pi }{2}(\because {\sin }^{-1}\frac{1}{x}+{\cos }^{-1}\frac{1}{x}=\frac{\pi }{2})$
$=1$
Ans : $\left(a\right)$