Cosinecos

Geometry Level 3

\[\tan \left[ \dfrac{\cos^{-1} \left( \sin \left( \cos^{-1}x \right) \right) + \sin^{-1} \left( \cos \left( \sin^{-1}x \right) \right)}{2} \right]= \, ?\]

Clarification: \(\sin^{-1}x \in \left[ 0, \frac{\pi}{2} \right]\).