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Math Help - Solving Identity (I always get half the solutions)

  1. #1
    s3a
    s3a is offline
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    Solving Identity (I always get half the solutions)

    cot (x) - cot^2 (x) = 0 x E [0,2pi]
    cot (x) = cot^2(x)
    cot (x) = 1
    tan (x) = 1
    x = tan-1(1)
    x = pi/4 + pi*n

    I get {pi/4, 5pi/4} but the answer is {pi/2, 3pi/2, pi/4, 5pi/4}

    In a lot of these types of questions, I keep getting half the solutions, is there a universal method that would allow me to always find all the possible values no matter the identity?

    (I don't know if "identity" is the right word for this since x can't be any value but I don't know what else to call it)

    Thanks in advance!
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  2. #2
    Member
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    you divided by cot(x).

    you can not divide by zero. so when you divide by cot(x), you must also set up a second equation:

    cot(x) = 0

    and then solve this to find the other solutions.
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