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sqrt((1 + sin)/(1 - sin)) type roots as sec + tan or cosec + cot

This type of question, asked 5 times: 21 Jul 2023 S2, 25 Jul 2023 S3, 12 Sep 2024 S1, 18 Sep 2024 S3, 19 Sep 2024 S3. All 5 questions below, oldest first.

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  1. Question 1

    21 Jul 2023 S2

    72
    Find the value of 1−sin⁡3θ1+sin⁡3θ\sqrt{\frac{1 - \sin 3\theta}{1 + \sin 3\theta}}.

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  2. Question 2

    25 Jul 2023 S3

    53
    The value of 1+cos⁡θ1−cos⁡θ\sqrt{\frac{1 + \cos\theta}{1 - \cos\theta}} is:

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  3. Question 3

    12 Sep 2024 S1

    72
    Find the value of the following expression. 1+sin⁡θ1−sin⁡θ\sqrt{\frac{1 + \sin\theta}{1 - \sin\theta}}

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  4. Question 4

    18 Sep 2024 S3

    62
    The given expression is equivalent to: sec⁡θ+1sec⁡θ−1+sec⁡θ−1sec⁡θ+1\sqrt{\frac{\sec\theta + 1}{\sec\theta - 1}} + \sqrt{\frac{\sec\theta - 1}{\sec\theta + 1}}

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  5. Question 5

    19 Sep 2024 S3

    68
    If A is an acute angle, then 1−cos⁡A1+cos⁡A+1+cos⁡A1−cos⁡A\sqrt{\frac{1 - \cos A}{1 + \cos A}} + \sqrt{\frac{1 + \cos A}{1 - \cos A}} is equal to:

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