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Trig equation with a modulus: number of solutions in an interval

This type of question, asked 2 times: 2021 Paper 9, 25 Jul 2022. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 9

    90
    The number of solutions of the equation ∣cot⁡x∣=cot⁡x+1sin⁡x|\cot x| = \cot x+\frac{1}{\sin x} in the interval [0,2π]\lbrack 0,2\pi\rbrack is

  2. Question 2

    25 Jul 2022

    78
    The number of solutions of ∣cos⁡x∣=sin⁡x|\cos x| = \sin x, such that −4π≤x≤4π- 4\pi \leq x \leq 4\pi is:

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