If x ^ 2 + y ^ 2 + 2x + 2Y + 1 = 0, then the value range of X + y is?

(x+1)^2+(y+1)^2=1
Let x + 1 = cosa
Then (y + 1) ^ 21 - (COSA) ^ 2 = (Sina) ^ 2
The range of sina is symmetric with respect to the origin
So let y + 1 = Sina
So x = cosa-1, y = sina-1
x+y=sina+cosa-2=√2sin(x+π/4)-2
-1

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