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Math Help - (cosx^2)/x=cosx true or false. Explain.

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    (cosx^2)/x=cosx true or false. Explain.

    For all real values of X.

    Is the following true or false? Provide reasoning for your answers.

    (cosx^2)/x=cosx

    I know it is false. Cos cannot be factored out of an expression.

    I just have a hard time coming up with the right words or proof why this is the case.
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  2. #2
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    Re: (cosx^2)/x=cosx true or false. Explain.

    Quote Originally Posted by StudentMCCS View Post
    For all real values of X.

    Is the following true or false? Provide reasoning for your answers.

    (cosx^2)/x=cosx

    I know it is false. Cos cannot be factored out of an expression.

    I just have a hard time coming up with the right words or proof why this is the case.
    it's not an identity, but is a valid conditional equation ...

    \frac{\cos^2{x}}{x} = \cos{x}

    \frac{\cos^2{x}}{x} - \cos{x} = 0

    \cos{x}\left(\frac{\cos{x}}{x} - 1\right) = 0

    \cos{x} = 0 ... lots of solutions

    \cos{x} = x ... one solution
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