The value of `(tan47^(@)+tan43^())/(1-tan47^(@)tan43^(@))` is

Options

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

Answer

To solve the expression \(\frac{\tan 47^\circ + \tan 43^\circ}{1 - \tan 47^\circ \tan 43^\circ}\), we can use the tangent addition formula. The formula states that:

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

### Step-by-step Solution:

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

2. **Apply the Tangent Addition Formula**:
According to the tangent addition formula, we have:
\[ \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \]
Therefore, substituting \( A \) and \( B \):
\[ \tan(47^\circ + 43^\circ) = \frac{\tan 47^\circ + \tan 43^\circ}{1 - \tan 47^\circ \tan 43^\circ} \]

3. **Calculate A + B**:
Now, calculate \( A + B \):
\[ 47^\circ + 43^\circ = 90^\circ \]

4. **Evaluate \(\tan(90^\circ)\)**:
We know that:
\[ \tan(90^\circ) \text{ is undefined (or infinite)} \]

5. **Conclusion**:
Therefore, the value of the given expression is:
\[ \frac{\tan 47^\circ + \tan 43^\circ}{1 - \tan 47^\circ \tan 43^\circ} = \tan(90^\circ) = \infty \]

### Final Answer:
The value of \(\frac{\tan 47^\circ + \tan 43^\circ}{1 - \tan 47^\circ \tan 43^\circ}\) is \(\infty\).