√ {frac{{1 - sin A}}{{1 + sin A}}} =

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3.Trigonometrical Ratios, Functions and Identities

easy

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

$\sec A + \tan A$

$\tan \left( {\frac{\pi }{4} - A} \right)$

$\tan \left( {\frac{\pi }{4} + \frac{A}{2}} \right)$

$\tan \left( {\frac{\pi }{4} - \frac{A}{2}} \right)$

Solution

(d) $\sqrt {\frac{{1 – \sin A}}{{1 + \sin A}}} = \sqrt {\frac{{1 – \cos \left( {\frac{\pi }{2} – A} \right)}}{{1 + \cos \left( {\frac{\pi }{2} – A} \right)}}} $

$ = \sqrt {\frac{{2{{\sin }^2}\left( {\frac{\pi }{4} – \frac{A}{2}} \right)}}{{2{{\cos }^2}\left( {\frac{\pi }{4} – \frac{A}{2}} \right)}}} = \tan \left( {\frac{\pi }{4} – \frac{A}{2}} \right)$.

Standard 11

Mathematics