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(sec theta - tan theta)/(sec theta + tan theta) = 1/k: find an expression in theta

This type of question, asked 2 times: 3 Feb 2022 Tier II, 18 Jan 2025 Tier II. All 2 questions below, oldest first.

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  1. Question 1

    3 Feb 2022 Tier II

    24
    If sec⁡θ−tan⁡θsec⁡θ+tan⁡θ=17\frac{\sec\theta - \tan\theta}{\sec\theta + \tan\theta} = \frac{1}{7}, θ\theta lies in first quadrant, then the value of cosec θ+cot⁡2θcosec θ−cot⁡2θ\frac{\text{cosec}\,\theta + \cot^2\theta}{\text{cosec}\,\theta - \cot^2\theta} is:

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  2. Question 2

    18 Jan 2025 Tier II

    19
    If sec⁡θ−tan⁡θsec⁡θ+tan⁡θ=19\frac{\sec\theta - \tan\theta}{\sec\theta + \tan\theta} = \frac{1}{9}, θ\theta lies in the first quadrant, then the value of sin⁡θ−tan⁡2θsin⁡θ+tan⁡2θ\frac{\sin\theta - \tan^2\theta}{\sin\theta + \tan^2\theta} is:

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