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Equation with no or few solutions, found by bounding both sides

This type of question, asked 3 times: 29 Jul 2022, 31 Jan 2024, 1 Feb 2024. All 3 questions below, oldest first.

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  1. Question 1

    29 Jul 2022

    162
    The number of elements in the set S={x∈R:2cos⁡(x2+x6)=4x+4−x}S =\left\{ x\in R:2\cos\left( \frac{x^{2}+ x}{6} \right)=4^{x}+4^{- x} \right\} is:

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  2. Question 2

    31 Jan 2024

    165
    The number of solutions, of the equation esin⁡x−2e−sin⁡x=2e^{\sin x}- 2e^{- \sin x}= 2 is

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  3. Question 3

    1 Feb 2024

    153
    The number of solutions of the equation 4sin⁡2x−44\sin^{2}x - 4 cos⁡3x+9−4cos⁡x=0;x∈[−2π,2π]\cos^{3}x + 9 - 4\cos x = 0;x \in \lbrack - 2\pi,2\pi\rbrack is:

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