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sec^2 - tan^2 = 1 hidden by a complementary angle: evaluate

This type of question, asked 3 times: 14 Jul 2023 S2, 20 Jul 2023 S1, 21 Jul 2023 S1. All 3 questions below, oldest first.

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  1. Question 1

    14 Jul 2023 S2

    72
    What is the value of sec⁡254∘−cot⁡236∘+32sin⁡237∘×sec⁡253∘+23tan⁡60∘\sec^2 54^\circ - \cot^2 36^\circ + \frac{3}{2}\sin^2 37^\circ \times \sec^2 53^\circ + \frac{2}{\sqrt{3}}\tan 60^\circ?

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  2. Question 2

    20 Jul 2023 S1

    59
    Solve the given expression. sec⁡2(90∘−θ)−cot⁡2θ2(sin⁡235∘+sin⁡255∘)\frac{\sec^2(90^\circ - \theta) - \cot^2\theta}{2(\sin^2 35^\circ + \sin^2 55^\circ)}

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  3. Question 3

    21 Jul 2023 S1

    60
    What is the value of sec⁡2θ−cot⁡2(90∘−θ)\sec^2\theta - \cot^2(90^\circ - \theta)?

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