Josh's trigonometric equations

Algebra Level 3

If xx and yy are real values such that 0xy1800^{\circ} \leq x-y \leq 180^{\circ} and

sinx+siny=1,cosx+cosy=2,\begin{aligned} \sin x + \sin y &= 1, \\ \cos x + \cos y & = \sqrt{2}, \end{aligned}

what is the value (in degrees) of xy x - y ?

This problem is posed by Josh P.

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