How do you prove the Law of Cosines?

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mom6

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In the following let (V, <, >) be a real inner product space. Prove the Law of Cosines:

llX - Yll^2 = llXll^2 + llYll^2 - 2llXllllYll cos Ѳ. Where X , Y ε V and Ѳ is the angle between X and Y. Please help me !!
 
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