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Trig x + 1/x = 2, so x = 1: evaluate or find the angle

This type of question, asked 4 times: 19 Sep 2024 S1, 19 Sep 2024 S3, 26 Sep 2024 S1, 19 Sep 2025 S1. All 4 questions below, oldest first.

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  1. Question 1

    19 Sep 2024 S1

    58
    The value of the expression sin⁡x+cosec⁡x=2\sin x + \operatorname{cosec} x = 2, then the value of sin⁡7x+cosec⁡7x\sin^7 x + \operatorname{cosec}^7 x is:

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  2. Question 2

    19 Sep 2024 S3

    67
    If tan⁡θ+cot⁡θ=2\tan \theta + \cot \theta = 2, and θ\theta is an acute angle, then the value of θ\theta is:

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  3. Question 3

    26 Sep 2024 S1

    64
    If A is an acute angle and tan⁡A+cot⁡A=2\tan A + \cot A = 2, find the value of 7tan⁡8A−6cot⁡8A+8sec⁡2A7\tan^8 A - 6\cot^8 A + 8\sec^2 A.

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  4. Question 4

    19 Sep 2025 S1

    64
    If tan⁡A+cot⁡A=2\tan A + \cot A = 2 and A∈(0,π/2)A \in (0, \pi/2), then what is sin⁡A+cos⁡A\sin A + \cos A?

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