If $\sin \left({\tan }^{-1}(x\sqrt{2})\right)=\cot \left({\sin }^{-1}\sqrt{1-{x}^{2}}\right),x\in \left(0,1\right)$, then the value of $x$ is: [JEE Main 2026, 6 Apr (Shift 2)]

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If \(\sin \left({\tan }^{-1}(x\sqrt{2})\right)=\cot \left({\sin }^{-1}\sqrt{1-{x}^{2}}\right),x\in \left(0,1\right)\), t…

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