Find the value of `costhetacos(90^(@)-theta)-sinthetasin(90^(@)-theta)`

Answer

To solve the problem, we need to find the value of the expression:

\[ \cos \theta \cos(90^\circ - \theta) - \sin \theta \sin(90^\circ - \theta) \]

### Step 1: Use the complementary angle identities
Recall the complementary angle identities:
- \(\cos(90^\circ - \theta) = \sin \theta\)
- \(\sin(90^\circ - \theta) = \cos \theta\)

### Step 2: Substitute the identities into the expression
Now, we can substitute these identities into our expression:

\[ \cos \theta \cdot \sin \theta - \sin \theta \cdot \cos \theta \]

### Step 3: Simplify the expression
Now, we can simplify the expression:

\[ \cos \theta \cdot \sin \theta - \sin \theta \cdot \cos \theta = 0 \]

### Final Answer
Thus, the value of the expression is:

\[ \boxed{0} \]

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