# Trigonometric inequality

1. Mar 21, 2009

### IsrTor

1. The problem statement, all variables and given/known data
solve the inequality:
-1$$\leq$$ 1$$/$$(1+cosx) $$\leq$$1

3. The attempt at a solution

firstly cosx does not equal -1 but you'll see doesn't help much
-1<cosx<1
0<cosx+1<2
that makes the above equation 1/(1+cosx) between 0.5 and infinity. but I have no clue as to how to find the set of x which solve the inequality

2. Mar 21, 2009

### tiny-tim

Hi IsrTor!

You need to learn your trigonometric identities …

what does 1 + cosx also equal?

3. Mar 21, 2009

### Staff: Mentor

Since 1/(1 + cosx) is between -1 and 1, its reciprocal has to be larger than 1 or smaller than -1, depending on whether 1/(1 + cos x) is positive or negative, respectively.

Can you do something with that?