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

AI Thread Summary
The discussion revolves around solving the inequality -1 ≤ 1/(1+cosx) ≤ 1. It is established that cosx cannot equal -1, leading to the conclusion that -1 < cosx < 1, which results in 1/(1+cosx) being between 0.5 and infinity. Participants suggest using trigonometric identities to further analyze the inequality. The reciprocal of the expression indicates that it must be either greater than 1 or less than -1, depending on its positivity or negativity. The conversation emphasizes the need for a deeper understanding of trigonometric functions to find the solution set for x.
IsrTor
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Homework Statement


solve the inequality:
-1\leq 1/(1+cosx) \leq1

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
 
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IsrTor said:
solve the inequality:
-1\leq 1/(1+cosx) \leq1

Hi IsrTor! :smile:

You need to learn your trigonometric identities …

what does 1 + cosx also equal? :wink:
 
IsrTor said:

Homework Statement


solve the inequality:
-1\leq 1/(1+cosx) \leq1

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?
 

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