Prove that: \[ \cos x+\sin \left(\frac{3 \pi}{2}+x\right)-\sin \left(\frac{3 \pi}{2}-x\right)+\c...

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Prove that:
\[
\cos x+\sin \left(\frac{3 \pi}{2}+x\right)-\sin \left(\frac{3 \pi}{2}-x\right)+\cos (\pi+x)=0 .
\]
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