If cosecA/(cosecA - 1) + cosecA/(cosecA + 1) = x, then x is

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

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

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

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

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

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

= $$\frac{2}{cos^2A} = 2sec^2A$$

=> Ans - (D)