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

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

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

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

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

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

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

= $$secA-tanA$$

=> Ans - (B)