How is the QM prediction derived for Bell's tests?

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Question 1: how is the QM prediction (i.e. cosine curve, shown below) derived for Bell's tests? in layman' termss

Question 2: while Malus's law, some physicists say, is not related to this cosine curve.
Is there an indirect/lengthy way to connect the two?
http://upload.wikimedia.org/wikipedia/commons/7/77/StraightLines.svg
 
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