What is the value of $$2sec^2A$$ ?

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

$$=\frac{\ 2}{\cos^2A}\times\frac{\ \sin^2A}{\sin^2A}$$

$$=\frac{\ 2\operatorname{cosec}^2A}{\cot^2A}$$

$$=\frac{\operatorname{cosec}^2A\ +\operatorname{cosec}A+\operatorname{cosec}^2A-\operatorname{cosec}A}{\operatorname{cosec}^2A-1}$$

$$=\frac{\operatorname{cosec}A\left(\operatorname{cosec}A\ +1\right)+\operatorname{cosec}A\left(\operatorname{cosec}A-1\right)}{\left(\operatorname{cosec}A+1\right)\left(\operatorname{cosec}A-1\right)}$$

$$=\frac{\operatorname{cosec}A}{\operatorname{cosec}A-1}+\frac{\operatorname{cosec}A}{\operatorname{cosec}A+1}$$

Hence, option C is the correct answer