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)

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