The value of (sin `20^(@) cos 70^(@)+sin70^(@) cos 20^(@) ` ) is ……….. .

Answer

To solve the expression \( \sin 20^\circ \cos 70^\circ + \sin 70^\circ \cos 20^\circ \), we can use the sine addition formula.

### Step-by-Step Solution:

1. **Recognize the Sine Addition Formula:**
The sine addition formula states that:
\[ \sin(a + b) = \sin a \cos b + \cos a \sin b \]
Here, we can let \( a = 20^\circ \) and \( b = 70^\circ \).

2. **Apply the Formula:**
Using the sine addition formula, we can rewrite the expression:
\[ \sin 20^\circ \cos 70^\circ + \sin 70^\circ \cos 20^\circ = \sin(20^\circ + 70^\circ) \]

3. **Calculate the Angle:**
Now, calculate \( 20^\circ + 70^\circ \):
\[ 20^\circ + 70^\circ = 90^\circ \]

4. **Evaluate the Sine of 90 Degrees:**
Now we find:
\[ \sin 90^\circ = 1 \]

5. **Final Result:**
Therefore, the value of \( \sin 20^\circ \cos 70^\circ + \sin 70^\circ \cos 20^\circ \) is:
\[ \boxed{1} \]