Prove that : \[ \sin \left(\frac{5 \pi}{6}+x\right)+\sin \left(\frac{5 \pi}{6}-x\right)=\cos x \]

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Prove that :
\[
\sin \left(\frac{5 \pi}{6}+x\right)+\sin \left(\frac{5 \pi}{6}-x\right)=\cos x
\]
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