First, I'm tempted to change to csc(x) and sec(x), but like many, maybe I'm not all that comfortable with those two functions.

Second, I'm tempted to multiply by sin(x), since sin(x) is never zero in the given interval. Maybe I'm lots more familar with the tangent function.

Third, maybe I'm tempted to get rid of the cosines by the Pythagorean Identity.

Not sure right off. What have you tried?