Question

Let $2si{n}^{2}x+3sinx-2$ >0 and $x^2-x-2$ < 0 (x is measured in radians). Then x lies in the Interval

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$2si{n}^{2}x+3sinx-2$ >0 $\Rightarrow (2sinx-1)(sinx+2)$ >0 $\Rightarrow 2sinx-1$ >0
$\Rightarrow sinx$ > $\frac{1}{2}\Rightarrow xϵ(\frac{\pi }{6},5\frac{\pi }{6})$
Also $x^2-x-2$ <0 $\Rightarrow (x-2)(x+1)$ <0 $\Rightarrow$ -1 < x < 2.
$\therefore xmustliein(\frac{\pi }{6},2)$