Let \cos \alpha+\cos \beta=2 and \sin \alpha+\sin \beta=0, where 0 \leq \alpha \leq 90^\circ, 0 \leq \beta \leq 90^\circ. What is the value of \cos 2\alpha-\cos 2\beta?

Explanation

The maximum value of \cos is 1. For \cos \alpha+\cos \beta=2 to hold true, \cos \alpha=1 and \cos \beta=1, which means \alpha=0^\circ and \beta=0^\circ. This also satisfies \sin \alpha+\sin \beta=0. Therefore, \cos 2(0^\circ) - \cos 2(0^\circ) = 1 - 1 = 0.

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