If ^ - 1 x + 2 ^ - 1 x = 2 3 , then x = - Vidyadip

MCQ

If ${\tan ^{ - 1}}x + 2{\cot ^{ - 1}}x = \frac{{2\pi }}{3},$ then $x =$

A
$\sqrt 2 $
B
$3$
✓
$\sqrt 3 $
D
$\frac{{\sqrt 3 - 1}}{{\sqrt 3 + 1}}$

✓

Answer

Correct option: C.

$\sqrt 3 $

c
(c) The given equation may be written as

${\tan ^{ - 1}}x + {\cot ^{ - 1}}x + {\cot ^{ - 1}}x = \frac{{2\pi }}{3}$

==> ${\cot ^{ - 1}}x = \frac{{2\pi }}{3} - \frac{\pi }{2}$ = $\frac{\pi }{6}$

==> $x = \sqrt 3 $.

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