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

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

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

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

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

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

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

= $$cosecA-cotA$$

=> Ans - (A)