The area of the region between the curves \(y = \sqrt{\frac{1 + sinx}{cosx}}\) and \(y = \sqrt{\frac{1 - sinx}{cosx}}\)bounded by the lines x = 0 & x = π/4 is
a. \(\int\limits_0^{\sqrt 2 - 1} \frac{t\,dt}{(1 + t^2)\sqrt {1-t^2}}\)
b. \(\int\limits_0^{\sqrt 2 - 1} \frac{4t}{(1 + t^2)\sqrt {1-t^2}}dt\)
c. \(\int\limits_0^{\sqrt 2 + 1} \frac{4t}{(1 + t^2)\sqrt {1-t^2}}dt\)
d. \(\int\limits_0^{\sqrt 2 + 1} \frac{t}{(1 + t^2)\sqrt {1-t^2}}dt\)
