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Ratios of complementary angles like cos A / sin(90 - A): each becomes 1, evaluate

This type of question, asked 6 times: 20 Jul 2023 S4, 10 Sep 2024 S3, 11 Sep 2024 S1, 11 Sep 2024 S2, 18 Sep 2024 S2, 25 Sep 2024 S1. All 6 questions below, oldest first.

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  1. Question 1

    20 Jul 2023 S4

    67
    Find the value of cos⁡41sin⁡49+sin⁡51cos⁡39\frac{\cos 41}{\sin 49} + \frac{\sin 51}{\cos 39}.

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  2. Question 2

    10 Sep 2024 S3

    63
    3sin⁡58∘5cos⁡32∘+2cos⁡62∘5sin⁡28∘\frac{3\sin 58^\circ}{5\cos 32^\circ} + \frac{2\cos 62^\circ}{5\sin 28^\circ} is equal to:

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  3. Question 3

    11 Sep 2024 S1

    55
    Find the value of sec⁡35∘cosec 55∘−cos⁡25∘sin⁡65∘\frac{\sec 35^\circ}{\text{cosec}\, 55^\circ} - \frac{\cos 25^\circ}{\sin 65^\circ}.

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  4. Question 4

    11 Sep 2024 S2

    62
    Evaluate the value of (cosec 56∘cos⁡34∘−cos⁡59∘ cosec 31∘)(\text{cosec}\,56^\circ \cos 34^\circ - \cos 59^\circ\, \text{cosec}\,31^\circ).

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  5. Question 5

    18 Sep 2024 S2

    55
    Find the value of tan⁡55∘cot⁡35∘\frac{\tan 55^\circ}{\cot 35^\circ}.

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  6. Question 6

    25 Sep 2024 S1

    54
    Evaluate 2tan⁡54∘cot⁡36∘−cot⁡41∘tan⁡49∘2\frac{\tan 54^\circ}{\cot 36^\circ} - \frac{\cot 41^\circ}{\tan 49^\circ}.

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