Given I=∫0π/2cosxcosx+sinxdxI = \int_0^{\pi/2} \frac{\sqrt{\cos x}}{\sqrt{\cos x} + \sqrt{\sin x}} dxI=∫0π/2cosx+sinxcosxdx, use the King's property to find the value of III.
π/4\pi/4π/4
π/2\pi/2π/2
000
111