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cos^-1 x + cos^-1 y + cos^-1 z = 3pi: each is -1, evaluate an expression

This type of question, asked 3 times: 4 May 2023 S2, 14 May 2024 S1, 15 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    4 May 2023 S2

    128
    If cos⁡−1x+cos⁡−1y+cos⁡−1z=3π\cos^{-1}x+\cos^{-1}y+\cos^{-1}z=3\pi, then the value of x2+y2+z2−2xyzx^2+y^2+z^2-2xyz is

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  2. Question 2

    14 May 2024 S1

    145
    If cos⁡−1x+cos⁡−1y+cos⁡−1z=3π\cos^{-1}x+\cos^{-1}y+\cos^{-1}z=3\pi, then the value of x2025+x2026+x2027x^{2025}+x^{2026}+x^{2027} is

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  3. Question 3

    15 May 2026 S1

    68
    If cos⁡−1x+cos⁡−1y+cos⁡−1z=3π\cos^{-1}x + \cos^{-1}y + \cos^{-1}z = 3\pi, then xy+yz+zxxy + yz + zx is equal to

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