1. ## Inequality.

I've got something like this:

I need to find $s$ that makes the following inequality true.

$\displaystyle\left|\frac{6s\cos x +1 - 6s}{-2s(\cos x -1) + 1}\right|\le 1$

Using some trig identities I got it down to $-4s\sin^2(x/2)-2\le -12s\sin^2(x/2)\le 4s\sin^2(x/2)$

which I think is correct, but I don't know what to do now...

2. If you put in s = 0 you will get equality. That works just fine if you are looking for one solution. However, there are more solutions and from what I was able to graph they all lie in the interval $s \in [0,t]$ for some real, positive number t.

3. Thanks, I worked it out by breaking the inequality into two separate ones and eventually found the answer to be s <= 1/4