Let \( g(x) \) be differentiable on \( R \) and \( \int_{\sin t}^{1...

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Let \( g(x) \) be differentiable on \( R \) and \( \int_{\sin t}^{1} x^{2} g(x) d x=(1-\sin t) \),
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W where \( t \in\left(0, \frac{\pi}{2}\right) \). Then the value of \( g\left(\frac{1}{\sqrt{2}}\right) \) is
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