The value of `(sin43^(@) Cos47^(@) + cos43^(@) sin47^(@)) ` is …….. .

Answer

To solve the expression \( \sin 43^\circ \cos 47^\circ + \cos 43^\circ \sin 47^\circ \), we can use the sine addition formula. The sine addition formula states that:

\[ \sin(A + B) = \sin A \cos B + \cos A \sin B \]

### Step-by-Step Solution:

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

2. **Apply the Sine Addition Formula**:
Using the sine addition formula, we can rewrite the expression:
\[ \sin 43^\circ \cos 47^\circ + \cos 43^\circ \sin 47^\circ = \sin(43^\circ + 47^\circ) \]

3. **Calculate \( 43^\circ + 47^\circ \)**:
\[ 43^\circ + 47^\circ = 90^\circ \]

4. **Evaluate \( \sin(90^\circ) \)**:
We know that:
\[ \sin(90^\circ) = 1 \]

5. **Final Answer**:
Therefore, the value of \( \sin 43^\circ \cos 47^\circ + \cos 43^\circ \sin 47^\circ \) is:
\[ \boxed{1} \]