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

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

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

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

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

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

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

= $$\sqrt{\frac{2}{sin^2\theta}}=\sqrt2cosec\theta$$

=> Ans - (B)