Evaluate
` sin 27 ^(@) sin 63 ^(@) - cos 63^(@) cos 27 ^(@) `

Answer

To evaluate the expression \( \sin 27^\circ \sin 63^\circ - \cos 63^\circ \cos 27^\circ \), we can use trigonometric identities to simplify the calculation. Here’s a step-by-step solution:

### Step 1: Rewrite the expression using trigonometric identities
We can use the identity for sine and cosine:
\[ \sin A \sin B - \cos A \cos B = -\cos(A + B) \]
In our case, let \( A = 27^\circ \) and \( B = 63^\circ \). Thus, we can rewrite the expression as:
\[ \sin 27^\circ \sin 63^\circ - \cos 63^\circ \cos 27^\circ = -\cos(27^\circ + 63^\circ) \]

### Step 2: Calculate \( 27^\circ + 63^\circ \)
Now, we calculate the sum:
\[ 27^\circ + 63^\circ = 90^\circ \]

### Step 3: Substitute back into the expression
Now we substitute back into our expression:
\[ -\cos(90^\circ) \]

### Step 4: Evaluate \( \cos(90^\circ) \)
We know that:
\[ \cos(90^\circ) = 0 \]
Thus, substituting this value gives:
\[ -\cos(90^\circ) = -0 = 0 \]

### Final Answer
Therefore, the value of the expression \( \sin 27^\circ \sin 63^\circ - \cos 63^\circ \cos 27^\circ \) is:
\[ \boxed{0} \]