$\sqrt{\frac{1 - s i n A}{1 + s i n A}}$ = ?

(a) sec A + tan A (b) sec A - tan A

(c) sec A tan A (d) none of these

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Solution

$\sqrt{\frac{1 - s i n A}{1 + s i n A}}$

= $\sqrt{\frac{1 - s i n A}{1 + s i n A}} \times \sqrt{\frac{1 - s i n A}{1 + s i n A}}$

= $\sqrt{\frac{(1 - s i n A)^{2}}{1 - s i n^{2} A}}$

= $\sqrt{\frac{(1 - s i n A)^{2}}{c o s^{2} A}}$

= $\frac{1 - s i n A}{c o s A}$

= $\frac{1}{c o s A} - \frac{s i n A}{c o s A}$

= $s e c A - t a n A .$

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Similar questions

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

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

(1 + c o t A + t a n A) (s i n A - c o s A) = s i n A t a n A - c o t A c o s A

\frac{tan A + sin A}{tan A - sin A} = \frac{sec A + 1}{sec A - 1}

\frac{tan A + sec A - 1}{tan A - sec A + 1} = sec A + tan A = \frac{1 + sin A}{cos A} = \sqrt{\frac{1 + sin A}{1 - sin A}}

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