#### Answer

$4$

#### Work Step by Step

$\left( \tan x+\cot x\right) ^{2}-\left( \tan x-\cot x\right) ^{2}=\left( \left( \tan x+\cot x\right) -\left( \tan x-\cot x\right) \right) \left( \left( \tan x+\cot \right) +\left( \tan x-\cot x\right) \right) $
$=2\cot x\times 2\tan x=4$