In the following match each item given under the Column I to its correct answer given under the Column II.
`{:(,"Column I",,"Column II"),((i),sin(x+y)sin(x-y),(a),cos^(2)x-sin^(2)y),((ii),cos(x+y)cos(x-y),(b),1-tantheta//1+tantheta),((iii),cot((pi)/(4)+theta),(c),1+tantheta//1-tantheta),((iv),tan((pi)/(4)+theta),(d),sin^(2)x-sin^(2)y):}`

Explanation

To solve the matching question, we will analyze each expression in Column I and find its corresponding expression in Column II step by step.

### Step 1: Match \( \sin(x+y) \sin(x-y) \)

1. **Use the product-to-sum identities**:
\[ \sin(x+y) \sin(x-y) = \frac{1}{2} [\cos(x-y) - \cos(x+y)] \]
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