Given $0 \le x \le \dfrac{1}{2}$ then the value of $\tan \left[ \sin^{-1} \left( \dfrac{x}{\sqrt{2}} + \dfrac{\sqrt{1-x^2}}{\sqrt{2}} \right) - \sin^{-1} x \right]$ is:
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Whenever you see $\frac{1}{\sqrt{2}}$ paired with $x$ and $\sqrt{1-x^2}$, it is a strong hint to use a compound angle formula involving $\pi/4$ (or $45^\circ$).