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. $(\frac{\pi }{6},\frac{5\pi }{6})$
  
• B. $(-1,\frac{5\pi }{6})$
  
• C. $(-1,2)$
  
• D. $(\frac{\pi }{6},2)$

Answer 1

The correct option is D

$(\frac{\pi }{6},2)$

$2si{n}^{2}x+3sinx-2>0$
$(2sinx-1)(sinx+2)>0$
$\Rightarrow 2sinx-1>0[\because -1\le sinx\le 1]$

$\Rightarrow sinx>\frac{1}{2}\Rightarrow x\in (\frac{\pi }{6},\frac{5\pi }{6})\left(i\right)$
Also $x^2-x-2<0$