If `cosalpha+cosbeta=0=sinalpha+sinbeta`, then prove that `cos2alpha +cos2beta=-2cos(alpha +beta)`.

Explanation

To prove that \( \cos 2\alpha + \cos 2\beta = -2\cos(\alpha + \beta) \) given that \( \cos \alpha + \cos \beta = 0 \) and \( \sin \alpha + \sin \beta = 0 \), we can follow these steps:

### Step 1: Use the given equations
We start with the equations:
\[ \cos \alpha + \cos \beta = 0 \quad \text{(1)} \]
\[
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