Answer
$tan 135^\circ=-\frac{\sqrt 2}{\sqrt 2}=-1$
$cot 135^\circ =\frac{1}{\tan 120^\circ}=-1$
Work Step by Step
From the table we have the following information:
$sin 135^\circ =\frac{\sqrt 2}{2}$
$cos 135^\circ=-\frac{\sqrt 2}{2}$
$sec 135^\circ =-\sqrt 2$
$csc 135^\circ =\sqrt 2$
then, using the elementary trigonometric identities we obtain:
$tan 135^\circ=-\frac{\sqrt 2}{\sqrt 2}=-1$
$cot 135^\circ =\frac{1}{\tan 120^\circ}=-1$