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

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

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

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

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

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

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

= $$\frac{2}{sin^2A} = 2cosec^2A$$

=> Ans - (A)