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Evaluate a combination of principal values of standard inverse-trig values

This type of question, asked 6 times: 4 May 2023 S2, 16 May 2023 S2, 10 May 2024 S2, 19 Apr 2025 S2, 13 Apr 2026 S1, 13 Apr 2026 S2. All 6 questions below, oldest first.

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  1. Question 1

    4 May 2023 S2

    116
    The value of tan⁡−1(3)−sec⁡−1(−2)cosec−1(−2)+cos⁡−1(−12)\frac{\tan^{-1}(\sqrt{3})-\sec^{-1}(-2)}{\text{cosec}^{-1}(-\sqrt{2})+\cos^{-1}\left(-\frac{1}{2}\right)} is

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  2. Question 2

    16 May 2023 S2

    141
    The value of tan⁡−1(−3)−sin⁡−112+cos⁡−1(−12)\tan^{-1}(-\sqrt{3}) - \sin^{-1}\dfrac{1}{\sqrt{2}} + \cos^{-1}\left(-\dfrac{1}{2}\right) is

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  3. Question 3

    10 May 2024 S2

    132
    The value of tan⁡−1(1)+cos⁡−1 ⁣(−12)+sin⁡−1 ⁣(−12)\tan^{-1}(1)+\cos^{-1}\!\left(-\dfrac{1}{2}\right)+\sin^{-1}\!\left(-\dfrac{1}{2}\right) is

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  4. Question 4

    19 Apr 2025 S2

    117
    The value of sin⁡−1(−12)+cos⁡−1(−12)− cot⁡−1(−13)+tan⁡−1(−3) is\sin^{- 1}\left( -\frac{1}{\sqrt{2}} \right)+\cos^{- 1}\left( -\frac{1}{2} \right)- \ \cot^{- 1}\left( -\frac{1}{\sqrt{3}} \right)+\tan^{- 1}( -\sqrt{3})\text{~is}

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  5. Question 5

    13 Apr 2026 S1

    69
    The value of tan⁡−1(3)+sec⁡−1(−2)−sin⁡−1(−12)\tan^{-1}(\sqrt{3}) + \sec^{-1}(-2) - \sin^{-1}\left(-\dfrac{1}{2}\right) is

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  6. Question 6

    13 Apr 2026 S2

    68
    The value of tan⁡−1(1)+cos⁡−1(12)+sin⁡−1(12)tan⁡−1(3)−sec⁡−1(−2)\dfrac{\tan^{-1}(1) + \cos^{-1}\left(\dfrac{1}{2}\right) + \sin^{-1}\left(\dfrac{1}{2}\right)}{\tan^{-1}(\sqrt{3}) - \sec^{-1}(-2)} is equal to

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