`(tan 35^(@))/(cot 55^(@))+(cot 78^(@))/(tan 12^(@))=?`

Options

A. `0`
B. `1`
C. `2`
D. none of these

Explanation

To solve the expression \((\tan 35^\circ)/(\cot 55^\circ) + (\cot 78^\circ)/(\tan 12^\circ)\), we can use trigonometric identities to simplify it step by step.

### Step-by-Step Solution:

1. **Rewrite the cotangent in terms of tangent**:
We know that \(\cot \theta = \frac{1}{\tan \theta}\). Therefore, we can rewrite \(\cot 55^\circ\) and \(\cot 78^\circ\):
\[ \cot 55^\circ = \frac{1}{\tan 55^\circ} \]
\[ \cot 78^\circ = \frac{1}{\tan 78^\circ} \]

2. **Substituting cotangent values**:
Substitute these values into the expression:
\[ \frac{\tan 35^\circ}{\frac{1}{\tan 55^\circ}} + \frac{\frac{1}{\tan 78^\circ}}{\tan 12^\circ} \]
This simplifies to:
\[ \tan 35^\circ \tan 55^\circ + \frac{1}{\tan 78^\circ \tan 12^\circ} \]

3. **Using the identity for tangent**:
We can use the identity \(\tan(90^\circ - \theta) = \cot \theta\). Thus, we have:
\[ \tan 55^\circ = \cot 35^\circ \]
Therefore, we can rewrite the first term:
\[ \tan 35^\circ \tan 55^\circ = \tan 35^\circ \cot 35^\circ = 1 \]

4. **Using the identity for cotangent**:
Similarly, for the second term, we can rewrite \(\tan 78^\circ\):
\[ \tan 78^\circ = \cot 12^\circ \]
Thus, we can rewrite the second term:
\[ \frac{1}{\tan 78^\circ \tan 12^\circ} = \frac{1}{\cot 12^\circ \tan 12^\circ} = 1 \]

5. **Combine the results**:
Now we can combine both results:
\[ 1 + 1 = 2 \]

### Final Answer:
The value of the expression is \(2\).