Question

$\sqrt{\frac{secA-\tan A}{secA+\tan A}}=?$
(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)

$$\begin{gathered} \sqrt{\frac{\sec A-\tan A}{\sec A+\tan A}} \\ \mathrm{By}\mathrm{rationalising},\mathrm{we}\mathrm{get}: \\ \sqrt{\frac{(\sec A-\tan A)}{(\sec A+\tan A)}\times \frac{(\sec A-\tan A)}{(\sec A-\tan A)}} \\ \text{=}\sqrt{\frac{(\sec A-\tan A)(\sec A-\tan A)}{({\sec }^{2}A-{\tan }^{2}A)}} \\ \text{=}\frac{(\sec A-\tan A)}{1}[\because {\text{sec}}^{2}A-{\text{tan}}^{2}A=1] \\ \text{=}\sec A-\tan A \end{gathered}$$