Prove that: \( \mathrm{P} \) (i) \( \cos \left(\frac{3 \pi}{2}+x\ri...

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Prove that:
\( \mathrm{P} \)
(i) \( \cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left[\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right]=1 \)
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(ii) \( \sin (\mathrm{n}+1) x \sin (\mathrm{n}+2) \mathrm{x}+\cos (\mathrm{n}+1) \mathrm{x} \cos (\mathrm{n}+2) \mathrm{x}=\cos \mathrm{x} \)
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