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Evaluate an expression of standard-angle values (30, 45, 60)

This type of question, asked 2 times: 15 Nov 2020 Tier II, 8 Aug 2022 Tier II. All 3 questions below, oldest first.

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  1. Question 1

    15 Nov 2020 Tier II

    29
    The value of cosec230∘sin⁡245∘+sec⁡260∘tan⁡60∘cosec245∘−sec⁡260∘tan⁡45∘\frac{\text{cosec}^2 30^\circ \sin^2 45^\circ + \sec^2 60^\circ}{\tan 60^\circ \text{cosec}^2 45^\circ - \sec^2 60^\circ \tan 45^\circ} is:

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  2. Question 2

    8 Aug 2022 Tier II

    9
    What is the value of 5sin⁡260∘+7sin⁡245∘+8cos⁡245∘5\sin^2 60^\circ + 7\sin^2 45^\circ + 8\cos^2 45^\circ?

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  3. Question 3

    8 Aug 2022 Tier II

    40
    What is the value of 3sin⁡230∘+35cos⁡260∘−2sec⁡245∘3\sin^2 30^\circ + \frac{3}{5}\cos^2 60^\circ - 2\sec^2 45^\circ?

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