2 ^ - 1 ( x) = ^ - 1 ( cose c ^2 x), then x = - Vidyadip

MCQ

$2{\tan ^{ - 1}}(\cos x) = {\tan ^{ - 1}}({\rm{cose}}{{\rm{c}}^2}x),$ then $ x =$

A
$\frac{\pi }{2}$
B
$\pi $
C
$\frac{\pi }{6}$
✓
$\frac{\pi }{3}$

✓

Answer

Correct option: D.

$\frac{\pi }{3}$

d
(d) $2{\tan ^{ - 1}}(\cos x)$$ = {\tan ^{ - 1}}(\cos {\rm{e}}{{\rm{c}}^2}x)$

==> ${\tan ^{ - 1}}\left( {\frac{{2\cos x}}{{1 - {{\cos }^2}x}}} \right) = {\tan ^{ - 1}}\left( {\frac{1}{{{{\sin }^2}x}}} \right)$

$ \Rightarrow \frac{{2\cos x}}{{{{\sin }^2}x}} = \frac{1}{{{{\sin }^2}x}}$

==> $2\cos x = 1$

$ \Rightarrow x = \frac{\pi }{3}$.

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