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Maximum value of a determinant with entries sin^2 x, cos^2 x and cos 2x

The same question, asked 2 times: 2021 Paper 6*, 2021 Paper 16. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 6

    61
    The maximum value of f(x)=∣sin⁡2x1+cos⁡2xcos⁡2x1+sin⁡2xcos⁡2xcos⁡2xsin⁡2xcos⁡2xsin⁡2x∣,x∈Rf(x) =\left| \begin{matrix} \sin^{2}x & 1 +\cos^{2}x & \cos2x \\ 1 +\sin^{2}x & \cos^{2}x & \cos2x \\ \sin^{2}x & \cos^{2}x & \sin2x \end{matrix} \right|,x\in R is:

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  2. Question 2

    2021 Paper 16

    54
    Let f(x)=∣sin⁡2x−2+cos⁡2xcos⁡2x2+sin⁡2xcos⁡2xcos⁡2xsin⁡2xcos⁡2x1+cos⁡2x∣;x∈(0,π]f(x) =\left| \begin{matrix} \sin^{2}x & - 2 +\cos^{2}x & \cos2x \\ 2 +\sin^{2}x & \cos^{2}x & \cos2x \\ \sin^{2}x & \cos^{2}x & 1 + \cos2x \end{matrix} \right|;x\in (0,\pi\rbrack. Then the maximum value of f(x)f(x) is?