If f(x) = 1 - x 1 + x , then f[f( ;2 )] = - Vidyadip

MCQ

If $f(x) = \frac{{1 - x}}{{1 + x}},$ then $f[f(\cos \;2\theta )] = $

A
$\tan 2\theta $
B
$\sec 2\theta $
✓
$\cos 2\theta $
D
$\cot 2\theta $

✓

Answer

Correct option: C.

$\cos 2\theta $

c
(c) $f[f(\cos \,\,2\theta )] = f\,\left[ {\frac{{1 - \cos \,\,2\theta }}{{1 + \cos \,\,2\theta }}} \right]$

$ = f({\tan ^2}\theta ) = \frac{{1 - {{\tan }^2}\theta }}{{1 + {{\tan }^2}\theta }} = \cos \,\,2\theta .$

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