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Equations using sin^-1 x + cos^-1 x = pi/2 (and cosec^-1 of the reciprocal)

This type of question, asked 6 times: 15 May 2023 S2, 16 May 2023 S1, 9 May 2024 S1, 19 Apr 2025 S1, 20 Apr 2026 S2, 13 May 2026 S1. All 6 questions below, oldest first.

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  1. Question 1

    15 May 2023 S2

    114
    If sin⁡−1x13+cosec−11312=π2\sin^{-1}\frac{x}{13} + \text{cosec}^{-1}\frac{13}{12} = \frac{\pi}{2}, then the value of xx is

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  2. Question 2

    16 May 2023 S1

    110
    If sin⁡−1 ⁣(x5)+csc⁡−1 ⁣(54)=π2\sin^{-1}\!\left(\frac{x}{5}\right) + \csc^{-1}\!\left(\frac{5}{4}\right) = \frac{\pi}{2}, then the value of x is

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  3. Question 3

    9 May 2024 S1

    146
    If sin⁡−1x+cos⁡−1y=3π10\sin^{-1}x+\cos^{-1}y=\frac{3\pi}{10}, then the value of cos⁡−1x+sin⁡−1y\cos^{-1}x+\sin^{-1}y is

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  4. Question 4

    19 Apr 2025 S1

    123
    If 4sin⁡−1x+cos⁡−1x=π4\sin^{- 1}x+\cos^{- 1}x=\pi then x=x=

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  5. Question 5

    20 Apr 2026 S2

    67
    If 2sin⁡−1x−3cos⁡−1x=42\sin^{-1}x - 3\cos^{-1}x = 4, then 2sin⁡−1x+3cos⁡−1x=2\sin^{-1}x + 3\cos^{-1}x =

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  6. Question 6

    13 May 2026 S1

    67
    If sin⁡−1(x5)+csc⁡−1(54)=π2\sin^{-1}\left(\dfrac{x}{5}\right) + \csc^{-1}\left(\dfrac{5}{4}\right) = \dfrac{\pi}{2}, then the value of xx is

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