For \( t \in(0,1) ; \) let \( x=\sqrt{2^{\sin ^{-1} t}} \) and \( y=\sqrt{2^{\cos -1} t} \), the...

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For \( t \in(0,1) ; \) let \( x=\sqrt{2^{\sin ^{-1} t}} \) and \( y=\sqrt{2^{\cos -1} t} \), then \( 1+\left(\frac{d y}{d x}\right)^{2} \) equals :
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