Can this sum of squares be negative?

Question

I must be tired, but could you please point to me what I am missing here:

$$ (\cos a + \cos b)^2 + (\sin a + \sin b)^2 = 2\cos a\cos b + 2\sin a\sin b = 2\cos(a-b) $$

Clearly the left hand side is non-negative, but the simplification leads to something that can be negative. I feel like it is staring me in the face, but I can't see it; am I doing something wrong?

Answer 1

You are missing $+2$ on the right side of your equality.