it should be sin x + sin y = a, cos x + cos y =a, then need to
find sin x + cos x.
sin x = a - sin y (1)
cos x = a - cosy (2)
So, using cos^2x + sin^2x = 1,
a^2 - 2cosy + cos^2 y + a^2 -2siny + sin^2 y = 1
==> 2a^2 -2cosy - 2siny = 0
So, 2 (cos y + sin y) = 2 a^2
==> cos y + sin y = a^2
Something like that, but I swap wrong way, so get in terms of y.
You can do opposite, then should get in terms of x.