If \({\rm{x}} + \frac{1}{{\rm{x}}} = 2{\rm{cos\alpha }}\), then the value of \({{\rm{x}}^2} + \frac{1}{{{{\rm{x}}^2}}}\) -

1
4 cos2α
2
4 cos2α - 1
3
2(cos2α - sin2α)
4
cos2α - sin2α

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