If `sinA=(sqrt(3))/(2)andsinB=(1)/(2)`, then find the value if sin AcosB +cosAsinB.

Answer

To solve the problem, we need to find the value of \( \sin A \cos B + \cos A \sin B \) given that \( \sin A = \frac{\sqrt{3}}{2} \) and \( \sin B = \frac{1}{2} \).

### Step-by-Step Solution:

1. **Identify Angles from Sine Values**:
- Given \( \sin A = \frac{\sqrt{3}}{2} \), we know that \( A = 60^\circ \) (since \( \sin 60^\circ = \frac{\sqrt{3}}{2} \)).
- Given \( \sin B = \frac{1}{2} \), we know that \( B = 30^\circ \) (since \( \sin 30^\circ = \frac{1}{2} \)).

2. **Calculate Cosine Values**:
- Now, we need to find \( \cos A \) and \( \cos B \).
- For \( A = 60^\circ \), \( \cos A = \cos 60^\circ = \frac{1}{2} \).
- For \( B = 30^\circ \), \( \cos B = \cos 30^\circ = \frac{\sqrt{3}}{2} \).

3. **Substitute Values into the Expression**:
- Now substitute \( A \) and \( B \) into the expression \( \sin A \cos B + \cos A \sin B \):
\[ \sin A \cos B + \cos A \sin B = \left(\frac{\sqrt{3}}{2}\right) \left(\frac{\sqrt{3}}{2}\right) + \left(\frac{1}{2}\right) \left(\frac{1}{2}\right) \]

4. **Perform the Multiplications**:
- Calculate \( \sin A \cos B \):
\[ \sin A \cos B = \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2} = \frac{3}{4} \]
- Calculate \( \cos A \sin B \):
\[ \cos A \sin B = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4} \]

5. **Add the Results**:
- Now add both results:
\[ \sin A \cos B + \cos A \sin B = \frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1 \]

### Final Answer:
Thus, the value of \( \sin A \cos B + \cos A \sin B \) is \( 1 \).