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在等式cos2x=2cos 2 x-1的两边对x求导（cos2x）′=（2cos 2 x-1）′。由求导法则得（-sin2x）·2=4cosx·（-sinx），化简后得等式sin2x=2sinxcosx。 （1）利用上述想法（或者其他方法），试由等式 （x∈R，整数n≥2）证明： 。 （2）对于整数，n≥3，求证： （i） ； （ii） ； （iii） 。
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