Tan frac{A}{2} is equal to

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3.Trigonometrical Ratios, Functions and Identities

easy

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

A

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

B

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

C

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

D

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

Solution

(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}}} $.

Standard 11

Mathematics

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