The problem is as follows:
Let the function:
$f(x)=\left|\frac{(\tan 6x+\tan 2x)(\cos 3x + \cos x )}{(\sin 6x)}\right|$
Assume $x\in \left\langle \frac{\pi}{4}, \frac{4\pi}{9}\right]-\left\{\frac{\pi}{3}\right]$
Find the maximum value which can take $f(x)$, using range analysis. Assume $f(x)$ gives values measured in hundreds of units.
The choices given in my workbook are as follows:
$\begin{array}{ll} 1.&195\\ 2.&198\\ 3.&199\\ 4.&200\\ \end{array}$
I'm really lost at how should I solve this problem. Since the problem indicates that this should be solved relying only in range analysis the thing is I don't know how to find the range for that function in the given:
$x\in \left\langle \frac{\pi}{4}, \frac{4\pi}{9}\right]-\left\{\frac{\pi}{3}\right]$
Thus I require help here. The only thing which I do recall is that absolute value will add a negative sign in front of whatever thing is inside if it is less than zero. Thus I believe that should be used here to see if it will have this sign in front for those functions in the given boundary for $x$. But I don't know how to use these ideas together.
I'm not sure if the multiplication of those function should be treated as intersection or what?. I'm confused as I explained how to get the range. As this problem is presented in my precalculus workbook thus an answer using such approach is the one which I'm intending to find.
Can someone guide me on what to do please, the answer which would help me the most is one which does explain step by step so I don't get confused with the solution. Thus, can this be solved without much fuss?.