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sin A + cos A (or sin A - cos A) given: square to get sin A cos A, then evaluate

This type of question, asked 8 times: 17 Jul 2023 S1, 17 Sep 2024 S2, 23 Sep 2024 S2, 17 Sep 2025 S1, 19 Sep 2025 S2, 19 Sep 2025 S3, 21 Sep 2025 S1, 22 Sep 2025 S3. All 8 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    17 Jul 2023 S1

    58
    If sin⁡t+cos⁡t=45\sin t + \cos t = \frac{4}{5}, then find sin⁡t.cos⁡t\sin t.\cos t.

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  2. Question 2

    17 Sep 2024 S2

    65
    If sin⁡A+cos⁡A=122\sin A + \cos A = \frac{1}{2\sqrt{2}}, then find the value of sin⁡4A+cos⁡4A\sin^4 A + \cos^4 A.

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  3. Question 3

    23 Sep 2024 S2

    55
    If sin⁡A−cos⁡A=3−22\sin A - \cos A = \frac{\sqrt{3} - \sqrt{2}}{2}, then the value of sin⁡A.cos⁡A\sin A.\cos A is:

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  4. Question 4

    17 Sep 2025 S1

    72
    If sin⁡A+cos⁡A=54\sin A + \cos A = \frac{5}{4}, find sin⁡2A\sin 2A.

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  5. Question 5

    19 Sep 2025 S2

    72
    If sin⁡A+cos⁡A=x\sin A + \cos A = x, then find the value of sin⁡2A+cos⁡2A+2sin⁡Acos⁡A\sin^2 A + \cos^2 A + 2\sin A\cos A.

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  6. Question 6

    19 Sep 2025 S3

    65
    If sin⁡x+cos⁡x=2\sin x + \cos x = \sqrt{2}, what is the value of sin⁡x−cos⁡x\sin x - \cos x?

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  7. Question 7

    21 Sep 2025 S1

    68
    If sin⁡A+cos⁡A=1\sin A + \cos A = 1, then find the value of sin⁡4A+cos⁡4A\sin^4 A + \cos^4 A.

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  8. Question 8

    22 Sep 2025 S3

    68
    If sin⁡A+cos⁡A=22\sin A + \cos A = \frac{\sqrt{2}}{2}, find the value of sin⁡2A+cos⁡2A+2sin⁡Acos⁡A\sin^2 A + \cos^2 A + 2\sin A \cos A.

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