Take into account that the given expressions can be written in terms of sine and cosine functions, as follow:
[tex]\begin{gathered} \cot 180=\frac{\cos180}{\sin180}=\frac{-1}{0}\colon\text{undefined} \\ \csc 180=\frac{1}{\sin 180}=\frac{1}{0}\colon\text{ undefined} \\ \cos 180=0 \\ \tan 180=\frac{\sin 180}{\cos 180}=\frac{0}{-1}=0 \\ \sec 180=\frac{1}{\cos 180}=\frac{1}{-1}=-1 \\ \sin 180=0 \end{gathered}[/tex]As you can notice, cot180 and csc180 are undefined
