Write down the value of: `cos68^(@) cos8^(@)+"sin"68^(@)"sin"8^(@)`

Answer

To solve the expression \( \cos 68^\circ \cos 8^\circ + \sin 68^\circ \sin 8^\circ \), we can use the cosine addition formula. Here are the steps:

### Step-by-Step Solution:

1. **Identify the Formula**:
We will use the cosine of the difference formula, which states:
\[ \cos(A - B) = \cos A \cos B + \sin A \sin B \]
In our case, let \( A = 68^\circ \) and \( B = 8^\circ \).

2. **Apply the Formula**:
Substitute \( A \) and \( B \) into the formula:
\[ \cos(68^\circ - 8^\circ) = \cos 68^\circ \cos 8^\circ + \sin 68^\circ \sin 8^\circ \]
This simplifies to:
\[ \cos(60^\circ) = \cos 68^\circ \cos 8^\circ + \sin 68^\circ \sin 8^\circ \]

3. **Calculate \( \cos(60^\circ) \)**:
We know that:
\[ \cos(60^\circ) = \frac{1}{2} \]

4. **Final Result**:
Therefore, we conclude that:
\[ \cos 68^\circ \cos 8^\circ + \sin 68^\circ \sin 8^\circ = \frac{1}{2} \]

### Final Answer:
\[ \cos 68^\circ \cos 8^\circ + \sin 68^\circ \sin 8^\circ = \frac{1}{2} \]