The area of the region between the curves $$y = \sqrt{\frac{1 + \sin x}{\cos x}}$$ and $$y = \sqrt{\frac{1 - \sin x}{\cos x}}$$ bounded by the lines x = 0 and $$x = \frac{\pi}{4}$$ is

A

$$\int_{0}^{\sqrt{2}-1}\frac{t}{(1+t^2)\sqrt{1-t^2}}dt$$

B

$$\int_{0}^{\sqrt{2}-1}\frac{4t}{(1+t^2)\sqrt{1-t^2}}dt$$

C

$$\int_{0}^{\sqrt{2}+1}\frac{4t}{(1+t^2)\sqrt{1-t^2}}dt$$

D

$$\int_{0}^{\sqrt{2}+1}\frac{t}{(1+t^2)\sqrt{1-t^2}}dt$$