Question

If $k \le \sin^{-1} x + \cos^{-1} x + \tan^{-1} x \le K$, then -

• A. $k = 0, K = \pi .$
• B. $k = 0, K = \pi / 2.$
• C. $k = \pi / 2 , K = \pi $
• D. None of these

Answer 1

Answer: (D)

$\sin^{-1} x + \cos^{-1}x +\tan^{-1}x = \frac{\pi}{2} + \tan^{-1} x$
Since domain of the function $x \in [-1, 1]$
$ \therefore - \frac{\pi}{4} \le \tan^{-1} x \le \frac{\pi}{4} $
Hence, $k = \frac{\pi}{4} K = \frac{3\pi}{4} $