If k ^ - 1 x + ^ - 1 x + ^ - 1 x K, then - Vidyadip

MCQ

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

✓
$k = 0,\,K = \pi $
B
$k = 0,K = \frac{\pi }{2}$
C
$k = \frac{\pi }{2},K = \pi $
D
None of these

✓

Answer

Correct option: A.

$k = 0,\,K = \pi $

a
(a) We have ${\sin ^{ - 1}}x + {\cos ^{ - 1}}x + {\tan ^{ - 1}}x = \frac{\pi }{2} + {\tan ^{ - 1}}x$

Since $\frac{{ - \pi }}{2} \le {\tan ^{ - 1}}x \le \frac{\pi }{2} $

$\Rightarrow 0 \le \frac{\pi }{2} + {\tan ^{ - 1}}x \le \pi $

$\therefore$ $K = \pi ,k = 0$.

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