A 2 is equal to - Vidyadip

MCQ

$\tan \frac{A}{2}$ is equal to

A
$ \pm \sqrt {\frac{{1 - \sin A}}{{1 + \sin A}}} $
B
$ \pm \sqrt {\frac{{1 + \sin A}}{{1 - \sin A}}} $
✓
$ \pm \sqrt {\frac{{1 - \cos A}}{{1 + \cos A}}} $
D
$ \pm \sqrt {\frac{{1 + \cos A}}{{1 - \cos A}}} $

✓

Answer

Correct option: C.

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

c
(c) $\tan \left( {\frac{A}{2}} \right) $

$= \frac{{\sin (A/2)}}{{\cos (A/2)}} $

$= \pm \sqrt {\frac{{(1 - \cos A)/2}}{{(1 + \cos A)/2}}} $

$= \pm \sqrt {\frac{{1 - \cos A}}{{1 + \cos A}}} $.

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