Question 95

What is the simplified value of $$\sqrt{\frac{1-sinA}{1+sinA}}$$ ?

Solution

Expression : $$\sqrt{\frac{1-sinA}{1+sinA}}$$

Rationalizing the denominator, we get :

= $$\sqrt{\frac{1-sinA}{1+sinA}}\times\sqrt{\frac{1-sinA}{1-sinA}}$$

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

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

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

= $$\frac{1}{cosA}-\frac{sinA}{cosA}=secA-tanA$$

=> Ans - (D)

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