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Integral of 1/(a + b cos x) by putting t = tan(x/2)

This type of question, asked 3 times: May 2022 S1, 11 May 2024 S1, 17 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    May 2022 S1

    101
    ∫π/43π/4dx1+cos⁡x\int_{\pi/4}^{3\pi/4} \frac{dx}{1+\cos x} is equal to

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  2. Question 2

    11 May 2024 S1

    101
    ∫0πdx4+3cos⁡x=\int_0^{\pi} \frac{dx}{4 + 3\cos x} =

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  3. Question 3

    17 Apr 2026 S2

    83
    The value of the definite integral ∫0π15+4cos⁡x dx\int_0^\pi\dfrac{1}{5 + 4\cos x}\,dx is equal to ...

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