\( 1 \leftarrow \) Verify the identity. \[ \cos (\alpha+\beta) \cos (\alpha-\beta)=\cos ^{2} \alpha-\sin ^{2} \beta \] Write the left side of the identity using the sum and difference formula. \( (\square)(\square) \) (Type the terms of your expression in the same order as they appear in the original expression.)

To verify the identity, we start with the left side of the equation: \[ \cos (\alpha + \beta) \cos (\alpha - \beta) \] Using the sum and difference formula for cosine, we can rewrite this as: \[ \left( \frac{1}{2} (\cos(\alpha + \beta) + \cos(\alpha - \beta)) \right)(\cos(\alpha - \beta)) \] We can express both terms using the identities: \[ \cos(\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta \] \[ \cos(\alpha - \beta) = \cos \alpha \cos \beta + \sin \alpha \sin \beta \] Thus, the complete expression becomes: \[ \frac{1}{2} ((\cos \alpha \cos \beta - \sin \alpha \sin \beta)(\cos \alpha \cos \beta + \sin \alpha \sin \beta)) \] So, in a simpler form, we can write the expression for verification. Now, the terms in the expression can be teamed up in the order they appear, as: \[ \cos \alpha \cos \beta \quad \text{and} \quad \sin \alpha \sin \beta \]