Question

The range of $si{n}^{-1}x+co{s}^{-1}x+ta{n}^{-1}x$ 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)

$si{n}^{-1}x+co{s}^{-1}x=\frac{\pi }{2}$,
$-1\le x\le 1$
$\Rightarrow \frac{-\pi }{4}\le ta{n}^{-1}x\le \frac{\pi }{4}$
$\Rightarrow \frac{\pi }{4}\le \frac{\pi }{2}+ta{n}^{-1}x\le \frac{3\pi }{4}$
Then range is $\left[\frac{\pi }{4},\frac{3\pi }{4}\right]$.