If 2sin-1 x = sin-1 2x\(\sqrt{1-x^{2}}\) then x ∈ _______.

1
\(\left[-\frac{1}{\sqrt{2}}, 1\right]\)
2
[0, 1]
3
\(\left[\frac{1}{\sqrt{2}}, 1\right]\)
4
\(\left[-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right]\)

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