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sec x + cos x = k: find sec^2 x + cos^2 x

The same question, asked 2 times: 14 Jul 2023 S4*, 26 Jul 2023 S3. Every wording below, oldest first.

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  1. Question 1

    14 Jul 2023 S4

    67
    If sec⁡θ+cos⁡θ=32\sec\theta + \cos\theta = 32, then sec⁡2θ+cos⁡2θ\sec^2\theta + \cos^2\theta is _________.

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  2. Question 2

    26 Jul 2023 S3

    54
    If cos⁡x+sec⁡x=723\cos x + \sec x = \frac{7}{2\sqrt{3}}, then the value of cos⁡2x+sec⁡2x\cos^2 x + \sec^2 x will be ______.

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