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A Pythagorean identity reduces the expression to 1

This type of question, asked 4 times: 18 Jul 2023 S2, 20 Jul 2023 S4, 25 Jul 2023 S2, 24 Sep 2025 S2. All 4 questions below, oldest first.

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  1. Question 1

    18 Jul 2023 S2

    55
    The value of (1sin⁡θ+1tan⁡θ)(1sin⁡θ−1tan⁡θ)\left(\frac{1}{\sin\theta} + \frac{1}{\tan\theta}\right)\left(\frac{1}{\sin\theta} - \frac{1}{\tan\theta}\right) is:

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  2. Question 2

    20 Jul 2023 S4

    54
    What is the value of sec⁡2A−tan⁡2A\sec^2 A - \tan^2 A?

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  3. Question 3

    25 Jul 2023 S2

    53
    sec⁡θ1−sin⁡2θ=?\sec\theta\sqrt{1 - \sin^2\theta} = ?

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  4. Question 4

    24 Sep 2025 S2

    68
    If 1+cot⁡2θ=cosec2θ1 + \cot^2\theta = \text{cosec}^2\theta, then what is the value of cosec260∘−cot⁡260∘\text{cosec}^2 60^\circ - \cot^2 60^\circ?

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