If 2 ^ - 1 ( x) = ^ - 1 (2 cosec x), then x = - Vidyadip

MCQ

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

A
$\frac{{3\pi }}{4}$
✓
$\frac{\pi }{4}$
C
$\frac{\pi }{3}$
D
None of these

✓

Answer

Correct option: B.

$\frac{\pi }{4}$

b
(b) We have $2$ ${\tan ^{ - 1}}(\cos x) = {\tan ^{ - 1}}(2\cos {\rm{ec}}x)$

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

$\frac{{2\cos x}}{{{{\sin }^2}x}} = 2{\rm{cosec}}\,x \Rightarrow 2\cos x = 2\sin x$

or $\sin x = \cos x$

$ \Rightarrow x = \frac{\pi }{4}$.

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