What is the simplified value of $$\sqrt{\frac{1-sinA}{1+sinA}}$$ ?
Expression : $$\sqrt{\frac{1-sinA}{1+sinA}}$$
Rationalizing the denominator, we get :
=Â $$\sqrt{\frac{1-sinA}{1+sinA}}\times\sqrt{\frac{1-sinA}{1-sinA}}$$
= $$\sqrt{\frac{(1-sinA)^2}{(1+sinA)(1-sinA)}}$$
= $$\sqrt{\frac{(1-sinA)^2}{1-sin^2A}}$$
= $$\sqrt{\frac{(1-sinA)^2}{cos^2A}}=\frac{1-sinA}{cosA}$$
= $$\frac{1}{cosA}-\frac{sinA}{cosA}=secA-tanA$$
=> Ans - (D)
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