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(sin + cos)^2 + (sin - cos)^2 = 2

This type of question, asked 3 times: 19 Jul 2023 S1, 19 Jul 2023 S4, 25 Jul 2023 S3. All 3 questions below, oldest first.

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  1. Question 1

    19 Jul 2023 S1

    65
    Find the value of (sin⁡θ+cos⁡θ)2+(sin⁡θ−cos⁡θ)2(\sin\theta + \cos\theta)^2 + (\sin\theta - \cos\theta)^2.

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  2. Question 2

    19 Jul 2023 S4

    53
    If cos⁡x+sin⁡x=2cos⁡x\cos x + \sin x = \sqrt{2}\cos x, what is the value of (cos⁡x−sin⁡x)2+(cos⁡x+sin⁡x)2(\cos x - \sin x)^2 + (\cos x + \sin x)^2?

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  3. Question 3

    25 Jul 2023 S3

    74
    If r=15(sin⁡θ+cos⁡θ)r = 15(\sin\theta + \cos\theta) and s=16(sin⁡θ−cos⁡θ)s = 16(\sin\theta - \cos\theta), then the value of r2152+s2162\frac{r^2}{15^2} + \frac{s^2}{16^2} is ______.

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