Show that: `sin^2 alpha + sin^2 beta + 2sinalpha sinbeta cos(alpha+beta)=sin^2 (alpha+beta)`

Explanation

To prove the identity \( \sin^2 \alpha + \sin^2 \beta + 2 \sin \alpha \sin \beta \cos(\alpha + \beta) = \sin^2(\alpha + \beta) \), we will follow these steps:

### Step 1: Start with the left-hand side
We begin with the left-hand side of the equation:
\[ \sin^2 \alpha + \sin^2 \beta + 2 \sin \alpha \sin \beta \cos(\alpha + \beta) \]

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