Can the set of x be found for -1 ≤ 1/(1+cosx) ≤ 1?

[IsrTor]

Homework Statement

solve the inequality:
-1$$\leq$$ 1$$/$$(1+cosx) $$\leq$$1

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

 

[tiny-tim]

solve the inequality:
-1$$\leq$$ 1$$/$$(1+cosx) $$\leq$$1

Hi IsrTor!

You need to learn your trigonometric identities …

what does 1 + cosx also equal?

 

[Mark44]

Homework Statement

solve the inequality:
-1$$\leq$$ 1$$/$$(1+cosx) $$\leq$$1

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

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?