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Square root of (sec t - tan t)/(sec t + tan t) or (1 - sin t)/(1 + sin t)

This type of question, asked 3 times: CDS 1 2020, CDS 2 2022, CDS 2 2025. All 3 questions below, oldest first.

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  1. Question 1

    CDS 1 2020

    62
    What is sec⁡x−tan⁡xsec⁡x+tan⁡x\sqrt{\frac{\sec x - \tan x}{\sec x + \tan x}} equal to ?

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  2. Question 2

    CDS 2 2022

    60
    What is (1+sin⁡θcos⁡θ)2+(cos⁡θ1+sin⁡θ)2−2\sqrt{\left(\frac{1 + \sin\theta}{\cos\theta}\right)^2 + \left(\frac{\cos\theta}{1 + \sin\theta}\right)^2 - 2} equal to, where 0<θ<π20 < \theta < \frac{\pi}{2} ?

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  3. Question 3

    CDS 2 2025

    34
    What is (sec⁡θ−tan⁡θ)−1−sin⁡θ1+sin⁡θ(\sec\theta - \tan\theta) - \sqrt{\dfrac{1 - \sin\theta}{1 + \sin\theta}} equal to?

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