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Number of integers k for which 7 cos x + 5 sin x = 2k + 1 has a solution

The same question, asked 2 times: 9 May 2023 S2, 15 May 2023 S1. Every wording below, oldest first.

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  1. Question 1

    9 May 2023 S2

    125
    The number of integral values of k, for which the equation 7cos⁡x+5sin⁡x=2k+17\cos x + 5\sin x = 2k+1 has a solution, is

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  2. Question 2

    15 May 2023 S1

    131
    The number of integral values of kk for which the equation 7cos⁡x+5sin⁡x=2k+17\cos x+5\sin x=2k+1 has a solution, is

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