Prove that: \[ 2 \sin \frac{5 \pi}{12} \cos \frac{\pi}{12}=\frac{\sqrt{3}+2}{2} \]

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1-2-Switch (2017)
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Prove that:
\[
2 \sin \frac{5 \pi}{12} \cos \frac{\pi}{12}=\frac{\sqrt{3}+2}{2}
\]
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