sin `70^(@)cos 10^(@) - cos 70^(@) sin 10^(@) = ` _________

Answer

To solve the expression \( \sin 70^\circ \cos 10^\circ - \cos 70^\circ \sin 10^\circ \), we can use the sine subtraction formula.

### Step-by-step Solution:

1. **Identify the Sine Subtraction Formula**:
The sine subtraction formula states that:
\[ \sin(A - B) = \sin A \cos B - \cos A \sin B \]
Here, we can identify \( A = 70^\circ \) and \( B = 10^\circ \).

2. **Apply the Formula**:
Substitute \( A \) and \( B \) into the formula:
\[ \sin(70^\circ - 10^\circ) = \sin 70^\circ \cos 10^\circ - \cos 70^\circ \sin 10^\circ \]
This simplifies to:
\[ \sin 60^\circ \]

3. **Calculate \( \sin 60^\circ \)**:
We know from trigonometric values that:
\[ \sin 60^\circ = \frac{\sqrt{3}}{2} \]

4. **Final Answer**:
Therefore, the value of \( \sin 70^\circ \cos 10^\circ - \cos 70^\circ \sin 10^\circ \) is:
\[ \frac{\sqrt{3}}{2} \]

### Summary:
The expression simplifies to \( \frac{\sqrt{3}}{2} \).