Would someone please help me? I know that the set $$\{(x,y)\mid \cos(x+y)\geq \frac{\sqrt 2}{2}\}$$ is convex, but I am seeking for a simple proof?
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Your set $$S=\{(x,y)\mid \cos(x+y)\geq \frac{\sqrt 2}{2}\}$$ is not convex. $P_1=(0,0)\in S$ and $P_2=(2 \pi,0)\in S$ however $\frac{P_1+P_2}{2}\notin S$
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please add the restriction $-\frac{\pi}{4}\leq x+y \leq \frac{\pi}{4} $ – Ali Jul 19 '15 at 01:14