\(\displaystyle{{\tan{{\left({\frac{{{3}\pi}}{{{2}}}}\right)}}}^{{{c}}}=}{\tan{{270}}}°\)

As \(\displaystyle{270}°\) falls in the third quadrant, tan and cot are positive values

\(\displaystyle{\tan{{270}}}°={\tan{{\left({180}°+{90}°\right)}}}={\tan{{90}}}°=\infty\)

As \(\displaystyle{270}°\) falls in the third quadrant, tan and cot are positive values

\(\displaystyle{\tan{{270}}}°={\tan{{\left({180}°+{90}°\right)}}}={\tan{{90}}}°=\infty\)