<s>[INST] If $\sin x + \sin y = 1$ and $\cos x + \cos y = 0$, solve for $x$ and $y$ 
*

*$\sin x + \sin y = 1$

*$\cos x + \cos y = 0$


Any valid pair of $(x, y)$ is fine, as the restrictions on the board in the image below are obscured.
I got the question from chapter 26 of a comic called Yamada-kun.

How can I solve this equation?
 [/INST] HINT
Squaring both equations you get
$$
\sin^2 x + \sin^2 y + 2\sin x \sin y = 1\\
\cos^2 x + \cos^2 y + 2\cos x \cos y = 0
$$
Now add them together to get
$$
2 + 2 \sin x \sin y + 2 \cos x \cos y = 1
$$
or in other words
$$
\frac{-1}{2} = \cos x \cos y + \sin x \sin y = \cos (x-y)
$$
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