Evaluate :
`(2 tan 22 (1^(@))/( 2 ))/(1 - tan ^(2) 22 (1^(@))/( 2))`

Answer

To evaluate the expression

\[ \frac{2 \tan\left(22^{\circ} \cdot \frac{1}{2}\theta\right)}{1 - \tan^2\left(22^{\circ} \cdot \frac{1}{2}\theta\right)}, \]

we can use the double angle formula for tangent, which states:

\[ \tan(2\theta) = \frac{2\tan(\theta)}{1 - \tan^2(\theta)}. \]

### Step-by-Step Solution:

1. **Identify the angle**:
Let \(\theta = 22^{\circ}\). Then we have:
\[ 2\theta = 2 \cdot 22^{\circ} = 44^{\circ}. \]

2. **Rewrite the expression**:
Substitute \(\theta\) into the expression:
\[ \frac{2 \tan(22^{\circ})}{1 - \tan^2(22^{\circ})}. \]

3. **Use the double angle formula**:
According to the double angle formula:
\[ \tan(2\theta) = \tan(44^{\circ}) = \frac{2\tan(22^{\circ})}{1 - \tan^2(22^{\circ})}. \]

4. **Evaluate \(\tan(44^{\circ})\)**:
We know that:
\[ \tan(44^{\circ}) = 1. \]

5. **Conclusion**:
Therefore, we can conclude that:
\[ \frac{2 \tan(22^{\circ})}{1 - \tan^2(22^{\circ})} = \tan(44^{\circ}) = 1. \]

Thus, the value of the given expression is:

\[ \boxed{1}. \]