Question

The range of $sin^{-1}x + cos^{-1} x + tan^{-1} x$ is

• A. $[0, \pi]$
• B. $ \left[\frac{\pi }{4}, \frac{3\pi }{4}\right]$
• C. $[0, \pi)$
• D. $ \left[0, \frac{\pi }{2}\right]$

Answer 1

Answer: (B)

$sin^{-1}\, x\,+cos^{-1}\, x = \frac{\pi}{2}$,
$-1 \le x \le 1$
$\Rightarrow \frac{-\pi}{4} \le tan^{-1}\,x \le \frac{\pi }{4}$
$\Rightarrow \frac{\pi }{4} \le \frac{\pi }{2} + tan^{-1}\,x \le \frac{3\pi }{4}$
Then range is $\left[\frac{\pi }{4}, \frac{3\pi }{4}\right]$.