Question

Assertion :If $2si{n}^{2}x+3sinx-2>0$ and $x^2-x-2<0$, then $-1<x<2$ Reason: $x^2-x-2<0$ if $-1<x<2$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

Reason:
$x^2-x-2<0\Rightarrow x<\frac{1\pm \sqrt{9}}{2}=2,-1$
$\Rightarrow -1<x<2$ ..(1)
Assertion:
$2{\sin }^{2}x+3\sin x-2>0\sin x>\frac{-3\pm 5}{4}=\frac{1}{2},-2\sin x>\frac{1}{2}\Rightarrow x>\frac{\pi }{6}$ ...(2)
$\sin x<-2$ (not possible)
From (1) and (2)
$\frac{\pi }{6}<x<2$
Hence, assertion is false