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Range of an expression that reduces to sin 2t or cos 2t

This type of question, asked 3 times: CDS 1 2021, CDS 2 2021, CDS 1 2022. All 3 questions below, oldest first.

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  1. Question 1

    CDS 1 2021

    47
    If sin⁡θcos⁡θ=k\sin\theta \cos\theta = k, where 0≤θ≤π20 \le \theta \le \frac{\pi}{2}, then which one of the following is correct?

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  2. Question 2

    CDS 2 2021

    50
    What is the maximum value of 1+2sin⁡2θcos⁡2θ−sin⁡4θ−cos⁡4θ1+2\sin^2\theta\cos^2\theta-\sin^4\theta-\cos^4\theta where 0∘<θ<90∘0^\circ<\theta<90^\circ ?

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  3. Question 3

    CDS 1 2022

    48
    What is the minimum value of sin⁡4θ+cos⁡4θ−2sin⁡2θcos⁡2θ\sin^4\theta + \cos^4\theta - 2\sin^2\theta\cos^2\theta?

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