#### Answer

$\dfrac {\tan ^{2}t+1}{\tan tcsc^{2}t}=\tan t$

#### Work Step by Step

$\dfrac {\tan ^{2}t+1}{\tan tcsc^{2}t}=\dfrac {\dfrac {\sin ^{2}t}{\cos ^{2}t}+1}{\dfrac {\sin t}{\cos t}\dfrac {1}{\sin ^{2}t}}=\dfrac {\dfrac {1}{\cos ^{2}t}}{\dfrac {1}{\cos t\sin t}}=\dfrac {\cos t\sin t}{\cos ^{2}t}=\dfrac {\sin t}{\cos t}=\tan t$