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cot t + cos t = m and cot t - cos t = n: relate m and n

The same question, asked 2 times: CDS 2 2018*, CDS 2 2026. Every wording below, oldest first.

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  1. Question 1

    CDS 2 2018

    70
    If cot⁡θ(1+sin⁡θ)=4m\cot \theta (1 + \sin \theta) = 4m and cot⁡θ(1−sin⁡θ)=4n\cot \theta (1 - \sin \theta) = 4n, then which one of the following is correct ?

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  2. Question 2

    CDS 2 2026

    41
    If cot⁡θ+cos⁡θ=m\cot\theta + \cos\theta = m, cot⁡θ−cos⁡θ=n\cot\theta - \cos\theta = n, where 0<θ<π20 < \theta < \frac{\pi}{2}, then what is m2−n2mn\frac{m^2 - n^2}{\sqrt{mn}} equal to ?

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