Question

The range of $f(x) = \sin^{-1} \, x - \cos^{-1}$ is

• A. $[ 0, \pi ]$
• B. $ \left[ \frac{ -3 \pi}{2}, \frac{\pi}{2} \right]$
• C. $ \left[ \frac{ - \pi}{2}, \frac{\pi}{2} \right]$
• D. $ [ - \pi , \pi ]$

Answer 1

Answer: (B)

$\sin^{-1} x - \cos^{-1} x = \frac{\pi}{2} - 2 \cos^{-1} x , 0 \le \cos^{-1} x \le \pi$