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sin X = cos Y or tan X = cot Y, so X + Y = 90: solve for the unknown angle

This type of question, asked 11 times: 18 Jul 2023 S3, 25 Jul 2023 S4, 12 Sep 2024 S3, 24 Sep 2024 S1, 26 Sep 2024 S1, 14 Sep 2025 S3, 23 Sep 2025 S2, 23 Sep 2025 S3, 24 Sep 2025 S3, 26 Sep 2025 S1, 26 Sep 2025 S2. All 11 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    18 Jul 2023 S3

    59
    If sin⁡(5x−25∘)=cos⁡(5y+25∘)\sin(5x - 25^\circ) = \cos(5y + 25^\circ), where 5x−25∘5x - 25^\circ and 5y+25∘5y + 25^\circ are acute angles,then the value of (x+y)(x + y) is:

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  2. Question 2

    25 Jul 2023 S4

    55
    If cos⁡(40∘+x)=sin⁡30∘\cos(40^\circ + x) = \sin 30^\circ, then the value of xx is:

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  3. Question 3

    12 Sep 2024 S3

    56
    If tan⁡4θ.tan⁡6θ=1\tan 4\theta . \tan 6\theta = 1, where 6θ6\theta is an acute angle, then find the value of cot⁡5θ\cot 5\theta.

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  4. Question 4

    24 Sep 2024 S1

    72
    If sin⁡3A=cos⁡(A−26∘)\sin 3A = \cos(A - 26^\circ), then A = ________, where 3A is an acute angle.

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  5. Question 5

    26 Sep 2024 S1

    60
    If (48∘+k)(48^\circ + k) is an acute angle and sin⁡(48∘+k)=cos⁡13∘\sin(48^\circ + k) = \cos 13^\circ, what is the value of k(in ∘^\circ)?

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  6. Question 6

    14 Sep 2025 S3

    70
    If tan⁡A=cot⁡(2A−30∘)\tan A = \cot(2A - 30^\circ), then what is the value of A?

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  7. Question 7

    23 Sep 2025 S2

    72
    If sin⁡x=cos⁡(x+20∘)\sin x = \cos(x + 20^\circ), then what is the value of x?

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  8. Question 8

    23 Sep 2025 S3

    70
    If sin⁡x=cos⁡(2x−10∘)\sin x = \cos(2x - 10^\circ), find the value of x.

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  9. Question 9

    24 Sep 2025 S3

    72
    If sin⁡(x)=cos⁡(3x−30∘)\sin(x) = \cos(3x - 30^\circ), what is the value of xx?

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  10. Question 10

    26 Sep 2025 S1

    67
    If sin⁡x=cos⁡(3x−20∘)\sin x = \cos(3x - 20^\circ), what is the value of xx?

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  11. Question 11

    26 Sep 2025 S2

    72
    If sin⁡x=cos⁡y\sin x = \cos y and cos⁡x=sin⁡y\cos x = \sin y, then x+yx + y equals:

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