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cos t + sec t given: find another expression

This type of question, asked 3 times: CDS 2 2020, CDS 1 2021, CDS 1 2022. All 3 questions below, oldest first.

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  1. Question 1

    CDS 2 2020

    47
    If cos⁡θ+sec⁡θ=k\cos\theta + \sec\theta = k, then what is the value of sin⁡2θ−tan⁡2θ\sin^2\theta - \tan^2\theta ?

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  2. Question 2

    CDS 1 2021

    56
    If sec⁡θ+cos⁡θ=52\sec\theta + \cos\theta = \frac{5}{2}, where 0≤θ≤90∘0 \le \theta \le 90^\circ, then what is the value of sin⁡2θ\sin^2\theta?

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  3. Question 3

    CDS 1 2022

    49
    If cos⁡θ+sec⁡θ−2=0\cos\theta + \sec\theta - 2 = 0, where 0≤θ<π20 \le \theta < \frac{\pi}{2}, then what is the value of cos⁡4θ+sec⁡4θ−2\cos^4\theta + \sec^4\theta - 2?

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