Prove that ∫ dx/(1+√tan x)=π/4, x ∈[0,π/2]

Question

Prove that 

\(\int\limits_0^{\pi/2}\cfrac{dx}{(1+\sqrt{tan\,x)}}=\cfrac{\pi}{4}\)

∫ dx/(1+√tan x)=π/4, x  ∈[0,π/2]

Answer 1

\(y=\int\limits_0^{\pi/2}\cfrac{dx}{1+\sqrt{\frac{sinx}{cosx}}}dx\)

Use King theorem of definite integral