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Math Help - Find values of variable for which trigonometric expression takes only +ve values?

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    Super Member fardeen_gen's Avatar
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    Find values of variable for which trigonometric expression takes only +ve values?

    For what value of a in the interval \left[\frac{7\pi}{6},\frac{7\pi}{4}\right] does the quadratic expression x^2 \cot a + 2x\sqrt{\tan a} + \tan a, assume only positive values.
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  2. #2
    MHF Contributor red_dog's Avatar
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    First of all, \tan a\geq 0\Rightarrow x\in\left[\frac{7\pi}{6},\frac{5\pi}{4}\right]

    Then the discriminant must be negative:

    \Delta=b^2-4ac=4\tan a-4<0\Rightarrow\tan a<1\Rightarrow x\in\left[\frac{7\pi}{6},\frac{5\pi}{4}\right)
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