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Let P(x) be a polynomial with real coeff...

Let P(x) be a polynomial with real coefficients such that `P(sin^2x)`=`P(cos^2x)`, for all `xϵ[0,π/2]`. Consider the following statements.Then: `I. P(x) is an even function`. `II. P(x) can be expressed as a polynomial in (2x−1)^ 2` `III. P(x) is a polynomial of even degree`.

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