Home
Class 12
MATHS
2sin^2x+3sinx-2>0 and x^2-x-2<0. Find th...

`2sin^2x+3sinx-2>0 and x^2-x-2<0.` Find the solution set.

Text Solution

AI Generated Solution

To solve the inequalities \(2\sin^2 x + 3\sin x - 2 > 0\) and \(x^2 - x - 2 < 0\), we will break it down step by step. ### Step 1: Solve the inequality \(x^2 - x - 2 < 0\) 1. **Factor the quadratic expression**: \[ x^2 - x - 2 = (x - 2)(x + 1) \] ...
Promotional Banner

Similar Questions

Explore conceptually related problems

lim_(x to pi//6) (2sin^2x+sinx-1)/(2sin^2x-3sinx+1)=

Evaluate the following limits: lim_(x to(pi)/(6))(2sin^(2)x+sinx-1)/(2sin^(2)x-3sinx+1)

If f(x) = (sin^2x + 4sinx + 5)/(2 sin ^2x + 8 sin x + 8) , then range of f(x) is

Evaluate the following limits: lim_(xrarr pi//6)((2sin^(2)x+sinx-1))/((2sin^(2)x-3sinx+1))

What is lim_(xto(pi)/(6)) (2sin^(2)x+sinx-1)/(sin^(2)x-3sinx+1) to?

Which of the following set of values of x satisfies the equation 2^((2 sin^(2) x-3sinx +1))+2^((2-2 sin^(2)x+3 sin x))=9 ?