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Trig ratio of a multiple of an inverse-trig value (sin 2A, tan 2A, sin 3A)

This type of question, asked 4 times: May 2022 S1, 2 May 2023 S1, 2 May 2023 S2, 17 Apr 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    May 2022 S1

    113
    The value of sin⁡ ⁣(2sin⁡−10.8)\sin\!\left(2\sin^{-1} 0.8\right) is equal to

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  2. Question 2

    2 May 2023 S1

    141
    The value of sin⁡(2cos⁡−1(−35))\sin\left(2\cos^{-1}\left(-\dfrac{3}{5}\right)\right) is

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  3. Question 3

    2 May 2023 S2

    136
    The value of tan⁡ ⁣(2tan⁡−1 ⁣(5−1)/2)\tan\!\left(2\tan^{-1}\!\left(\sqrt{5}-1\right)/2\right) is

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  4. Question 4

    17 Apr 2026 S2

    65
    sin⁡(3sin⁡−1(15))=\sin\left(3\sin^{-1}\left(\dfrac{1}{5}\right)\right) =

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