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Math Help - Finding the sum, in radians, of the solutions for x

  1. #1
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    Finding the sum, in radians, of the solutions for x

    I am trying to solve a problem from a study manual for the NYSTCE. I think the manual might be breaking some mathematical laws. Someone please throw a life raft.

    The problem is as follows:
    What is the sum, in radians, of the solutions for x in the following equation?
    Tan2x = (3/2)(sec x)

    The manual gives a detailed explanation:

    It rewrites Tan2x as sec2x-1 to arrive at the equation below.
    sec2x-1 = (3/2) (sec x)

    The manual loses me when it writes the equation above then as:
    2sec2x - 3secx - 2 = 0

    How is this so? I am lost on this step. Maybe I am missing a rule. Help on this problem would be greatly appreciated.
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Finding the sum, in radians, of the solutions for x

    Quote Originally Posted by polcareb192 View Post
    I am trying to solve a problem from a study manual for the NYSTCE. I think the manual might be breaking some mathematical laws. Someone please throw a life raft.

    The problem is as follows:
    What is the sum, in radians, of the solutions for x in the following equation?
    Tan2x = (3/2)(sec x)

    The manual gives a detailed explanation:

    It rewrites Tan2x as sec2x-1 to arrive at the equation below.
    sec2x-1 = (3/2) (sec x)

    The manual loses me when it writes the equation above then as:
    2sec2x - 3secx - 2 = 0

    How is this so? I am lost on this step. Maybe I am missing a rule. Help on this problem would be greatly appreciated.
    There are a couple of steps in front of that last equation.
    sec2x-1 = (3/2) (sec x)

    1) Multiply both sides by 2.

    2) Get everything to one side.

    -Dan
    Thanks from adkinsjr
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  3. #3
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    Re: Finding the sum, in radians, of the solutions for x

    No, they just multiplied throughout by 2 and then rearranged so you can solve like a quadratic.
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  4. #4
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    Re: Finding the sum, in radians, of the solutions for x

    I thank you. The manual skips steps and makes it difficult at times to follow detailed explanations. Much appreciated.
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