Answer
$1$
Work Step by Step
$\cot \alpha =\cot \left( \alpha -2\pi k\right)
\\\Rightarrow \cot \dfrac {17\pi }{4}=\cot \left( \dfrac {17\pi }{4}-4\pi \right)
\\=\cot \dfrac {\pi }{4}
\\=\dfrac {\cos \frac {\pi }{4}}{\sin \frac {\pi }{4}}
\\=\dfrac {\frac {\sqrt {2}}{2}}{\frac {\sqrt {2}}{2}}
\\=1$
