\[ \sin^{-1}\left ( x - \frac{x^2}{2} + \frac{x^3}{4} - \cdots \right ) + { \cos^{-1}\left ( { x^2 - \frac{x^4}{2} + \frac{x^6}{4} \cdots} \right ) } = { \frac{\pi }{2}} \]

Given the equation above for \(0<|x|<2^{0.5}\), then \(x\) equals to:

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