The value of `(tan 47^(@) + tan 43^(@))/(1-tan 47^(@) tan 43^(@))` is

Options

A. 1
B. 0
C. `infty`
D. `-1`

Answer

To solve the expression \((\tan 47^\circ + \tan 43^\circ)/(1 - \tan 47^\circ \tan 43^\circ)\), we can use the trigonometric identity for the tangent of the sum of two angles. The identity states:

\[ \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \]

### Step-by-Step Solution:

1. **Identify the Angles**:
Let \( A = 47^\circ \) and \( B = 43^\circ \).

2. **Apply the Identity**:
According to the identity mentioned, we can write:
\[ \tan(A + B) = \tan(47^\circ + 43^\circ) = \tan(90^\circ) \]

3. **Calculate the Sum of Angles**:
\[ 47^\circ + 43^\circ = 90^\circ \]

4. **Evaluate \(\tan(90^\circ)\)**:
The tangent of \(90^\circ\) is undefined (or can be considered as infinity). Therefore:
\[ \tan(90^\circ) = \text{undefined} \]

5. **Conclusion**:
Thus, the value of the expression \((\tan 47^\circ + \tan 43^\circ)/(1 - \tan 47^\circ \tan 43^\circ)\) is undefined.

### Final Answer:
The value of \((\tan 47^\circ + \tan 43^\circ)/(1 - \tan 47^\circ \tan 43^\circ)\) is undefined.