Let `2sin^2x+3sinx-2>0 andx^2-x-2<0(x` is measured in radians). Then `x` lies in the interval (a)`(pi/6,(5pi)/6)` (b) `(-1,(5pi)/6)` (c)`(-1,2)` (d) `(pi/6,2)`

Explanation

`2sin^2x+3sinx-2>0`

`2sin^2x+4sinx-sinnx-2>0`

`2sinx(sinx+2)-1(sinx+2)>0`

`(2sin-1)(sinx+2)>0`

`2sinx-1>0`

`sinx>1/2`

`x^2-x-2<0`

`x^2-2x+x-2<0`

...