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 expression using complementary angles
We know from trigonometric identities that:
\[ \tan(90^\circ - \theta) = \cot(\theta) \]
In our case, we can express \( 55^\circ \) as \( 90^\circ - 35^\circ \). Therefore, we can rewrite \( \tan(55^\circ - A) \) as:
\[ \tan(90^\circ - 35^\circ - A) = \cot(35^\circ + A) \]

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

### Step 3: Simplify the expression
Since we have \( \cot(35^\circ + A) - \cot(35^\circ + A) \), this simplifies to:
\[ 0 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{0} \]

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