Evaluate : `(tan 23^(@)) xx ( tan 67^(@)) `

Answer

To evaluate the expression \((\tan 23^\circ) \times (\tan 67^\circ)\), we can use the trigonometric identity that relates tangent and cotangent.

### Step-by-Step Solution:

1. **Identify the relationship between angles**:
We know that \(67^\circ\) can be expressed in terms of \(23^\circ\):
\[ 67^\circ = 90^\circ - 23^\circ \]

2. **Use the co-function identity**:
The co-function identity states that:
\[ \tan(90^\circ - \theta) = \cot(\theta) \]
Therefore, we can write:
\[ \tan(67^\circ) = \cot(23^\circ) \]

3. **Substitute the identity into the expression**:
Now we can substitute \(\tan(67^\circ)\) in the original expression:
\[ (\tan 23^\circ) \times (\tan 67^\circ) = (\tan 23^\circ) \times (\cot 23^\circ) \]

4. **Use the relationship between tangent and cotangent**:
We know that:
\[ \cot(\theta) = \frac{1}{\tan(\theta)} \]
Thus, we can write:
\[ \tan 23^\circ \times \cot 23^\circ = \tan 23^\circ \times \frac{1}{\tan 23^\circ} \]

5. **Simplify the expression**:
This simplifies to:
\[ \tan 23^\circ \times \frac{1}{\tan 23^\circ} = 1 \]

### Final Answer:
Therefore, the value of \((\tan 23^\circ) \times (\tan 67^\circ)\) is:
\[ \boxed{1} \]