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Math Help - another domain question

  1. #1
    Super Member
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    Smile another domain question

    hi
    i need a little help with this domain question
    let  f(x)=\tan (x)-\sqrt{\tan^{2}(x)-\tan (x)}
    such that x \in ]\frac{-\pi}{2},\frac{+\pi}{2}[
    this is how i started :
     D = \left \{ x\in ]\frac{-\pi}{2},\frac{+\pi}{2}[\mid tan^{2}(x)-tan(x)\geq 0 \right \}
    next step :
    \forall x\in ]\frac{-\pi}{2},\frac{+\pi}{2}[ we have tan^{2}(x)-tan(x) positive and so tan(x) \in ]-\infty ,0]\cup [1,+\infty [
    what should i do next ?
    thanks a lot
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Raoh View Post
    hi

    \forall x\in ]\frac{-\pi}{2},\frac{+\pi}{2}[ we have tan^{2}(x)-tan(x) positive
    \forall x\in ]0,\frac{+\pi}{4}[ we have tan^{2}(x)-tan(x) NEGATIVE
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  3. #3
    No one in Particular VonNemo19's Avatar
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    \uparrow You've already stated the answer! \uparrow

    I mean, it would be more explicit if you wrote what values of x are implied by tan^2(x)-tanx\geq0.

    Do you know how to do that?
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  4. #4
    Super Member
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    Smile

    hi
    well ..we have tan^2(x)-tanx\geq0 which means tan(x) \in (- \infty ,0] \cup [1,+ \infty ),and so x \in (\frac{-\pi}{2},0]\cup [\frac{\pi}{4},\frac{+\pi}{2})
    am i right ?
    thanks
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