Let 2{sin ^2}x + 3sin x - 2 0 and {x^2} | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(d) $2\,{\sin ^2}x + 3\,\sin x - 2 > 0$

$2\,{\sin ^2}x + 4\,\sin x - \sin x - 2 > 0$

$2\,\sin x\,(\sin x + 2) - 1\,(\sin x + 2) > 0$

Vedclass · Accepted Answer

$\left( {\frac{\pi }{6},\;2} \right)$

Vedclass · Answer

(d) $2\,{\sin ^2}x + 3\,\sin x - 2 > 0$ $2\,{\sin ^2}x + 4\,\sin x - \sin x - 2 > 0$ $2\,\sin x\,(\sin x + 2) - 1\,(\sin x + 2) > 0$ $\,(\sin x + 2)\,(2\sin x - 1) > 0$ $2\,\sin x - 1 > 0\,\, \Rightarrow \,\,\sin x > 1/2$ $x > \pi /6\,\, \Rightarrow \,\,x \in \,\,(\pi /6,\,\,\infty ).....(i)$ and ${x^2} - x - 2 < 0\, \Rightarrow \,{x^2} - 2x + x - 2 < 0$ $x\,(x - 2) + 1\,(x - 2) < 0$ $(x + 1)\,(x - 2) < 0\, \Rightarrow \,\,x \in ( - 1,\,\,2).....(ii)$ From $(i)$ and $(ii)$, $x \in (\pi /6,\,\,2)$.

Let $2{\sin ^2}x + 3\sin x - 2 > 0$ and ${x^2} - x - 2 < 0$ ($x$ is measured in radians). Then $x$ lies in the interval

Similar Questions

If the range of $f(x) = \frac{2x^2-14x^2-8x+49}{x^4-7x^2-4x+23}$ is ($a, b$], then ($a +b$) is

The range of the polynomial $P(x)=4 x^3-3 x$ as $x$ varies over the interval $\left(-\frac{1}{2}, \frac{1}{2}\right)$ is

Domain of the function $f(x) = {\sin ^{ - 1}}\left( {\frac{{2 - |x|}}{4}} \right) + {\cos ^{ - 1}}\left( {\frac{{2 - |x|}}{4}} \right) + {\tan ^{ - 1}}\left( {\frac{{2 - |x|}}{4}} \right)$ is

Let $f$ be a function defined on the set of all positive integers such that $f(x y)=f(x)+f(y)$ for all positive integers $x, y$. If $f(12)=24$ and $f(8)=15$. The value of $f(48)$ is

The total number of functions,$f:\{1,2,3,4\} \cdot\{1,2,3,4,5,6\}$ such that $f (1)+ f (2)= f (3)$, is equal to .