Prove that \[ \sum_{k=1}^{n-1}{ }^{n} C_{k}[\cos k x \cdot \cos (n+k) x+\sin (n-k) x \cdot \sin ...
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0Prove that
\[
\sum_{k=1}^{n-1}{ }^{n} C_{k}[\cos k x \cdot \cos (n+k) x+\sin (n-k) x \cdot \sin (2 n-k) x]=
\]
\( \left(2^{n}-2\right) \cos n x \).
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