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

**fardeen_gen** · May 23rd 2009, 10:03 PM

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.

**red_dog** · May 24th 2009, 05:16 AM

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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