It is normally best to write all of your sec(x), csc(x), tan(x), and cot(x) in terms of sin(x) and cos(x). That way, if anything cancels, you can simplify the expression.

Hey, there's a sin(x) on the top as well as the bottom! So, as long as the sin(x) is not zero, we're ok to divide the top and bottom by sin(x) and cancel them.

So which angles have a cosine value of ?

Once you've deduced what x is, don't forget, you can't have any angles that would let sin(x) be equal to zero. So you'll have to examine your answers and refuse any answers that had a sin value of zero.