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1/(cosec t + cot t) - 1/sin t given: find the expression with cosec t - cot t

The same question, asked 2 times: CDS 2 2022*, CDS 2 2026. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2022

    57
    If 1cosec⁡θ−cot⁡θ−1sin⁡θ=x\frac{1}{\operatorname{cosec}\theta - \cot\theta} - \frac{1}{\sin\theta} = x, then what is 1cosec⁡θ+cot⁡θ−1sin⁡θ\frac{1}{\operatorname{cosec}\theta + \cot\theta} - \frac{1}{\sin\theta} equal to, where 0<θ<π20 < \theta < \frac{\pi}{2} ?

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  2. Question 2

    CDS 2 2026

    42
    If 1cosec⁡θ+cot⁡θ−1sin⁡θ=p\frac{1}{\operatorname{cosec}\theta + \cot\theta} - \frac{1}{\sin\theta} = p, then what is 1sin⁡θ−1cosec⁡θ−cot⁡θ\frac{1}{\sin\theta} - \frac{1}{\operatorname{cosec}\theta - \cot\theta} equal to ?

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