Evaluate :
`tan (55^(@)-A)-cot (35^(@)+A)`

Answer

To evaluate the expression \( \tan(55^\circ - A) - \cot(35^\circ + A) \), we can follow these steps:

### Step 1: Rewrite the cotangent term
We know that:
\[ \cot(90^\circ - \theta) = \tan(\theta) \]
Using this identity, we can rewrite \( \cot(35^\circ + A) \):
\[ \cot(35^\circ + A) = \tan(90^\circ - (35^\circ + A)) = \tan(55^\circ - A) \]

### Step 2: Substitute the cotangent term into the expression
Now, we can substitute this back into our original expression:
\[ \tan(55^\circ - A) - \cot(35^\circ + A) = \tan(55^\circ - A) - \tan(55^\circ - A) \]

### Step 3: Simplify the expression
Now, we can simplify the expression:
\[ \tan(55^\circ - A) - \tan(55^\circ - A) = 0 \]

### Final Answer
Thus, the value of the expression \( \tan(55^\circ - A) - \cot(35^\circ + A) \) is:
\[ \boxed{0} \]