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Value of cos^-1[(cos(9pi/10) - sin(9pi/10))/sqrt2]

The same question, asked 2 times: 9 May 2023 S1, 25 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    9 May 2023 S1

    117
    The value of cos⁡−1 ⁣(12(cos⁡9π10−sin⁡9π10))\cos^{-1}\!\left(\frac{1}{\sqrt{2}}\left(\cos\frac{9\pi}{10}-\sin\frac{9\pi}{10}\right)\right) is

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  2. Question 2

    25 Apr 2025 S1

    117
    The principal value of cos⁡−1[12(cos⁡9π10−sin⁡9π10)]\cos^{- 1}\left\lbrack \frac{1}{\sqrt{2}}\left( \cos\frac{9\pi}{10}- \sin\frac{9\pi}{10} \right) \right\rbrack is

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