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Take \begin{align} 1-\sqrt{ 1-x^2} &= (1-\sqrt{ 1-x^2})\frac{1+\sqrt{ 1-x^2}}{1+\sqrt{ 1-x^2}}\\ &= \frac{x^2}{1+\sqrt{ 1-x^2}} \end{align} So \begin{align} y = x\sqrt{\frac{1}{2+2\sqrt{1-x^2}}} \end{align}


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