The solution set of the equation ^ - 1 x = 2 ^ - 1 x is - Vidyadip

MCQ

The solution set of the equation ${\sin ^{ - 1}}x = 2{\tan ^{ - 1}}x$ is

A
$\{1, 2\}$
B
$\{-1, 2\}$
✓
$\{-1,1, 0\}$
D
$\{1, \frac{1}{2} , 0\}$

✓

Answer

Correct option: C.

$\{-1,1, 0\}$

c
(c) ${\sin ^{ - 1}}x = 2{\tan ^{ - 1}}x$

==> ${\sin ^{ - 1}}x = {\sin ^{ - 1}}\frac{{2x}}{{1 + {x^2}}}$

$ \Rightarrow \frac{{2x}}{{1 + {x^2}}} = x$ ==> ${x^3} - x = 0$

==> $x(x + 1)(x - 1) = 0$ ==> $x = \left\{ { - 1,\,\,1,\,\,0} \right\}$.

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