Question

\[ \tan x+\cot(\pi+x)+\cot\left(\frac{\pi}{2}+x\right)+\cot(2\pi-x) \]

\[ \text{is equal to} \]

Solution

Using identities

\[ \cot(\pi+x)=\cot x \]

\[ \cot\left(\frac{\pi}{2}+x\right)=-\tan x \]

\[ \cot(2\pi-x)=-\cot x \]

Substituting,

\[ \tan x+\cot x-\tan x-\cot x \]

\[ =0 \]

Answer

\[ \boxed{0} \]