If A 2 = 3 2 , then 1 + A 1 - A = - Vidyadip

MCQ

If $\tan \frac{A}{2} = \frac{3}{2},$ then $\frac{{1 + \cos A}}{{1 - \cos A}} = $

A
$ - 5$
B
$5$
C
$9/4$
✓
$4/9$

✓

Answer

Correct option: D.

$4/9$

d
(d) Given that $\tan \frac{A}{2} = \frac{3}{2}$.

$\frac{{1 + \cos A}}{{1 - \cos A}} $

$= \frac{{2{{\cos }^2}\frac{A}{2}}}{{2{{\sin }^2}\frac{A}{2}}} $

$= {\cot ^2}\frac{A}{2} = {\left( {\frac{2}{3}} \right)^2} = \frac{4}{9}$.

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