SOLUTION: Find all x in the interval (0, pi) that satisfy: cot(x/2)>1+cot(x)

Question 1015049: Find all x in the interval (0, pi) that satisfy:
cot(x/2)>1+cot(x)
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
We know that , and so by inverting,
.
The original inequality then becomes

, or

.
==>
The fact that x is in (0,pi) means that x/2 is in (0, pi/2), in which case tan(x/2) is always POSITIVE and so the last inequality becomes
.
==> , or .
The last inequality is always true except when 1 - tan(x/2) = 0. This happens only when , or .
Therefore, the solution set of the inequality is (0,pi/2) U (pi/2,pi).
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