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If maximum and minimum values of the det...

If maximum and minimum values of the determinant `|{:(1+sin^2x,cos^2x,sin2x),(sin^2x,1+cos^2x,sin2x),(sin^2x,cos^2x,1+sin2x):}|`
are `alpha and beta` then show that `(alpha^(2n)-beta^(2n))` is always an even integer for `n in N`.

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