Question

Find the sum of value of x for which ${\sec }^{-1}x+{\sin }^{-1}x=\frac{\pi }{2}$.

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is A 0

We know that ${\sec }^{-1}x$ is defined for $x\in (-\infty ,-1)\cup (1,\infty )$

But ${\sin }^{-1}x$ is defined for $x\in [-1,1]$

Hence, ${\sec }^{-1}x+{\sin }^{-1}x=\frac{\pi }{2}$ for $x=\pm 1$