Question 96

What is the value of √[(1 + sinA)/(1 - sinA)]?

Solution

Expression : $$\sqrt{[\frac{(1 + sinA)}{(1 - sinA)}}]$$

Multiplying both numerator and denominator by $$(\sqrt{1+sinA})$$

= $$\sqrt{[\frac{(1 + sinA)}{(1 - sinA)}}]$$ $$\times \sqrt{\frac{(1+sinA)}{(1+sinA)}}$$

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

= $$\frac{1+sinA}{cosA} = (\frac{1}{cosA}+\frac{sinA}{cosA})$$

= $$secA+tanA$$

=> Ans - (C)

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What is the value of √[(1 + sinA)/(1 ­- sinA)]?