#### Answer

$sec^{2}xcsc^{2}x$

#### Work Step by Step

$\left( \tan x+\cot x\right) ^{2}=\tan ^{2}x+\cot ^{2}x+2\tan x\cot x=\tan ^{2}x+\cot ^{2}x+2$
$=\tan ^{2}x+1+\cot ^{2}x+1=\dfrac {1}{\cos ^{2}x}+\dfrac {1}{\sin ^{2}x}=\dfrac {\cos ^{2}x+\sin ^{2}x}{\cos ^{2}x\sin ^{2}x}=\dfrac {1}{\cos ^{2}x\sin ^{2}x}=sec^{2}xcsc^{2}x$