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Value of cos(2 cos^-1 x + sin^-1 x) at x = 1/5

The same question, asked 2 times: 2 May 2023 S1, 10 May 2023 S2. Every wording below, oldest first.

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  1. Question 1

    2 May 2023 S1

    105
    The value of cos⁡(2cos⁡−1x+sin⁡−1x)\cos\left(2\cos^{-1}x + \sin^{-1}x\right) at x=15x = \frac{1}{5}, where 0≤cos⁡−1x≤π0 \le \cos^{-1}x \le \pi and −π2≤sin⁡−1x≤π2-\frac{\pi}{2} \le \sin^{-1}x \le \frac{\pi}{2}, is

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  2. Question 2

    10 May 2023 S2

    130
    The value of cos⁡(2cos⁡−1x+sin⁡−1x)\cos(2\cos^{-1}x + \sin^{-1}x) at x=15x = \frac{1}{5} is

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