You didn't put in any parentheses to show where the
numerators and denominators begin and end.

However this equation cannot be an identity regardless
of where the parentheses should go -- because
suppose A=45° and B=45°.  Then 

tan(A) = tan(B) = cot(A) = cot(B) = 1 

The above becomes:

TANA+COTB/COTA+TANB=TANA+COTB

           1+1/1+1 = 1+1

Theis is no way to put parentheses in the left side to
make that equation true.

Edwin