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Q.
If $k \le \sin^{-1} x + \cos^{-1} x + \tan^{-1 } x \le K$, then
Inverse Trigonometric Functions
Solution:
We have,
$\sin^{-1} x + \cos^{-1} x +\tan^{-1} x = \frac{\pi}{2} + \tan^{-1} x$
Now $\sin^{-1} \, x$ and $\cos^{-1} x$ are defined only if $-1 \le x \le 1 $
So, $ - \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}$
$ \therefore k = \frac{\pi}{4}$ and $k = \frac{3\pi}{4} $