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　$n$を正の整数とする．
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\item[(1)]次の式を簡単にせよ．
\[ \sin x \{ \cos x+\cos3x+\cdots\cdots+\cos(2n-1)x \} \]
\item[(2)]次の式を証明せよ．
\[ \cos x+\cos3x+\cdots\cdots+\cos(2^{n+1}-3)x+\cos(2^{n+1}-1)x \]
\[ =2^n\cos x\cdot\cos2x\cdots\cdots\cos2^{n-1}x\cdot\cos2^nx \]
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