Domain of f(x) = sec x + cot x

How about we put f(x) in this form:
f(x)=1cosx+cosxsinx\displaystyle f(x) = \frac{1}{cosx} + \frac{cosx}{sinx}

Can you see where the function is undefined?
 
If you put it in that form, then cos x and sin x cannot equal zero. Then x cannot equal pi/2 or zero...is that correct? If so how do you write that as a union, that is the form my teacher wants the answer in
 
Well there are more solutions to cosx = 0 and sinx = 0. For cosx, what happens if x = 3pi/2? 5pi/2? 7pi/2? etc. etc. For sinx, what happens if x = pi? 2pi? 3pi? 4pi? etc. etc.

You mean in interval notation? I think set notation would be better if you are considering ALL solutions for x. In your question, is there a restriction on what x could be? Such as 0≤x≤2π\displaystyle 0 \leq x \leq 2\pi?
 
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