Question

What is \( \cos^{-1} x + \sec^{-1} 1 \)?

• A. \( \frac{\pi}{2} \)
• B. \( \frac{\pi}{3} \)
• C. 0
• D. \( \infty \)

Hint:

The value of \( \sec^{-1} 1 \) is \( 0 \), and \( \cos^{-1} x + 0 = \frac{\pi}{2} \) if \( x = 1 \).

Answer 1

The Correct Option is A

We are asked to find: \[ \cos^{-1} x + \sec^{-1} 1 \] First, recall that: \[ \sec^{-1} 1 = 0 \] This is because the secant function is equal to 1 when the angle is \( 0 \). Thus, the expression simplifies to: \[ \cos^{-1} x + 0 = \frac{\pi}{2} \] Thus, the correct answer is \( \frac{\pi}{2} \).