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Range of sin^2 t + cos^4 t

The same question, asked 2 times: CDS 2 2016, CDS 1 2021. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2016

    78
    If A=sin⁡2θ+cos⁡4θA = \sin^2\theta + \cos^4\theta where 0≤θ<π20 \le \theta < \frac{\pi}{2}, then which one of the following is correct ?

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  2. Question 2

    CDS 1 2021

    48
    If p=sin⁡2θ+cos⁡4θp = \sin^2 \theta + \cos^4 \theta for 0≤θ≤π20 \le \theta \le \frac{\pi}{2}, then consider the following statements : 1. pp can be less than 34\frac{3}{4}. 2. pp can be more than 1. Which of the above statements is/are correct?

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