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tan x + sec x = 2 cos x: solutions in [0, 2pi] or general solution

The same question, asked 3 times: 9 May 2023 S1*, 11 May 2023 S2*, 10 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    9 May 2023 S1

    141
    In (0,2π)(0,2\pi), the number of solutions of tan⁡θ+sec⁡θ=2cos⁡θ\tan\theta+\sec\theta=2\cos\theta are

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  2. Question 2

    11 May 2023 S2

    132
    The number of solutions of tan⁡x+sec⁡x=2cos⁡x\tan x+\sec x=2\cos x in [0,2π][0,2\pi] is

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  3. Question 3

    10 May 2024 S1

    138
    Number of solutions of tan⁡x+sec⁡x=2cos⁡x\tan x+\sec x=2\cos x in [0,2π][0,2\pi]

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