What is the value of [sec θ/(sec θ - 1)] + [sec θ/(sec θ + 1)] ?

Expression : $$\frac{sec\theta}{sec\theta-1}+\frac{sec\theta}{sec\theta+1}$$

= $$\frac{sec\theta(sec\theta+1)+sec\theta(sec\theta-1)}{(sec\theta-1)(sec\theta+1)}$$

= $$\frac{(sec^2\theta+sec\theta)+(sec^2\theta-sec\theta)}{sec^2\theta-1}$$

Using, $$(sec^2\theta-tan^2\theta=1)$$

= $$\frac{2sec^2\theta}{tan^2\theta}=2sec^2\theta cot^2\theta$$

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

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

=> Ans - (C)