Evaluate each of the following :
`cos60^(@)cos30^(@)-sin60^(@)sin30^(@)`

Options

A. 1
B. 0
C. -1
D. `1/2`

Answer

To evaluate the expression \( \cos 60^\circ \cos 30^\circ - \sin 60^\circ \sin 30^\circ \), we can use the cosine angle addition formula. Here are the steps:

### Step 1: Identify the angles
We have:
- \( A = 60^\circ \)
- \( B = 30^\circ \)

### Step 2: Apply the cosine angle addition formula
The cosine angle addition formula states:
\[ \cos A \cos B - \sin A \sin B = \cos(A + B) \]
So, we can rewrite our expression as:
\[ \cos 60^\circ \cos 30^\circ - \sin 60^\circ \sin 30^\circ = \cos(60^\circ + 30^\circ) \]

### Step 3: Calculate the angle
Now, calculate \( 60^\circ + 30^\circ \):
\[ 60^\circ + 30^\circ = 90^\circ \]

### Step 4: Evaluate \( \cos 90^\circ \)
Now we need to find \( \cos 90^\circ \):
\[ \cos 90^\circ = 0 \]

### Conclusion
Thus, the value of the expression \( \cos 60^\circ \cos 30^\circ - \sin 60^\circ \sin 30^\circ \) is:
\[ \boxed{0} \]