The value of \(\int_{0}^{\frac{\pi}{2}} \frac{\sqrt{\tan x}}{\sqrt{\tan x}+\sqrt{\cot x}}dx\) is

\(\frac{\pi}{2}\) \(\frac{\pi}{4}\) \(\frac{\pi}{8}\) None of these

\(\frac{\pi}{4}\)

\(\int_{a}^{b}f(x)dx=\int_{a}^{b}f(a+b-x)dx\)