1. 3cot^2 (x) - 1 = 0
My answer: pi/3, 2pi/3, 4pi/3, 5pi/3

2. 4cos^2 (x) - 1 = 0
My answer: pi/3, 2pi/3, 5pi/3, 4pi/3

3. 2sin (x) + csc (x) = 0
My answer: unknown lol
i got to the part: sin^2 (x) = -1/2

4. 4sin^3 (x) + 2sin^2 (x) - 2sin^2 (x) = 1

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  1. 3. 2sin (x) + csc (x) = 0
    My answer: unknown lol
    i got to the part: sin^2 (x) = -1/2
    I do not know what to do either. There is no real solution.

    4 looks like a typo. The second two terms are identical and cancel each other.
    Are you sure it is not:
    4 sin^3 x + 2 sin^2 x - 2 sin x = 1 ???
    if so
    let y = sin x
    4 y^3 + 2 y^2 -2 y - 1 = 0
    factor that
    (2y+1) works
    (2y+1)(2 y^2-1) = 0
    y = sin x = -1/2
    y = sin x = + ( sqrt 2) /2
    y = sin x = - (sqrt 2) / 2
    You can do it from there

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  2. Thank you!

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