Solve this


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

(a) (sec A + tan A)
(b) (sec A − tan A)
(c) sec A tan A
(d) None to these



(b) (sec A − tan A)

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

$=\sqrt{\frac{(1-\sin A)}{(1+\sin A)} \times \frac{(1-\sin A)}{(1-\sin A)}} \quad$ [Multiplying the denominator and numerator by $\left.(1-\sin A)\right]$

$=\frac{(1-\sin A)}{\sqrt{1-\sin ^{2} A}}$

$=\frac{(1+\sin A)}{\sqrt{\cos ^{2} A}}$

$=\frac{(1-\sin A)}{\cos A}$

$=\frac{1}{\cos A}-\frac{\sin A}{\cos A}$

$=\sec A-\tan A$


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