Answer
$-1$
Work Step by Step
Period of $tan$ function is $\pi$
It means
$tan\left( \alpha \right) =tan\left( \alpha +\pi k\right) =tan\left( \alpha -\pi k\right) $
$k$ is integer number
$\tan \dfrac {23\pi }{4}=\tan \left( 5\pi +\dfrac {3\pi }{4}\right) =\tan \left( \dfrac {3\pi }{4}\right) =\dfrac {\sin \dfrac {3\pi }{4}}{\cos \dfrac {3\pi }{4}}=\dfrac {\dfrac {\sqrt {2}}{2}}{\dfrac {-\sqrt {2}}{2}}=-1 $
