It would be great if someone can help me solve this!
For the domain, just remember that you can't divide something by 0, so x for which the denominator is = 0 may not be in the domain ! That's nearly all you need here.
In other cases, you may need to know that, for example, you can't have a negative number under a square root.
For the range, you may need this information : -1 <= cos(x) (or sin(x)) <= 1