Question

$\sqrt{\frac{1+\sin A}{1-\sin A}}=?$
(a) (sec A + tan A)
(b) (sec A − tan A)
(c) sec A tan A
(d) None of these

Answer 1

(a) (sec A + tan A)

$$\begin{gathered} \sqrt{\frac{1+\text{sin}A}{1-\text{sin}A}} \\ \text{=}\sqrt{\frac{(1+\text{sin}A)}{(1-\text{sin}A)}\times \frac{(1+\text{sin}A)}{(1+\text{sin}A)}}\left[\text{Multiplying and dividing by}(1+\text{sin}A)\right] \\ \text{=}\frac{(1+\text{sin}A)}{\sqrt{1-{\text{sin}}^{2}A}} \\ \text{=}\frac{(1+\text{sin}A)}{\sqrt{{\text{cos}}^{2}A}} \\ \text{=}\frac{(1+\text{sin}A)}{\text{cos}A} \\ \text{=}\frac{1}{\text{cos}A}+\frac{\text{sin}A}{\text{cos}A} \\ \text{=sec}A+\tan A \end{gathered}$$