#### Answer

$\dfrac {csct+1}{csct-1}=\left( sect+\tan t\right) ^{2}$

#### Work Step by Step

$\dfrac {csct+1}{csct-1}=\dfrac {\dfrac {1}{\sin t}+1}{\dfrac {1}{\sin t}-1}=\dfrac {1+\sin t}{1-\sin t}=\dfrac {\left( 1+\sin t\right) \left( 1+\sin t\right) }{\left( 1-\sin t\right) \left( 1+\sin t\right) }=\left( \dfrac {1+\sin t}{\cos t}\right) ^{2}=\left( sect+\tan t\right) ^{2}$