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(sin t - cos t + 1)/(sin t + cos t - 1) equals sec t + tan t

The same question, asked 2 times: CDS 1 2020, CDS 1 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2020

    60
    What is sin⁡θ−cos⁡θ+1sin⁡θ+cos⁡θ−1−sin⁡θ+1cos⁡θ\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} - \frac{\sin\theta + 1}{\cos\theta} equal to ?

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  2. Question 2

    CDS 1 2024

    52
    If sin⁡θ−cos⁡θ+1sin⁡θ+cos⁡θ−1=psec⁡θ+qtan⁡θ\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = p\sec\theta + q\tan\theta, where 0<θ<π20 < \theta < \frac{\pi}{2}, then what is p+qp + q equal to ?

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