Tangent of integration - ظل التكامل

Let $x = sin(u)$ and $dx = cos(u) du$ , $0 \le u \le \frac{\pi}{2}.$ The above integral expression becomes:

$tan [\large{\int^{\frac{\pi}{2}}_{0} \sqrt{1 - sin^{2}(u)} cos(u) \, du}]$ ;

or $tan [\large{\int^{\frac{\pi}{2}}_{0} cos^{2}(u) \, du}]$ ;

or $tan [\large{\int^{\frac{\pi}{2}}_{0} \frac{1}{2} + \frac{1}{2} \cdot cos(2u) \, du}]$ ;

or $tan [\frac{u}{2} + \frac{1}{4} \cdot sin(2u)]$ , $0 \le u \le \frac{\pi}{2}$ ;

or $tan(\frac{\pi}{4})$ ;

or $\boxed{1}.$