证明cos 2x cos x=1/2(cos x+cos 3x)

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/09 15:33:59

证明：等式右边=1/2(cosx+cos2x*cosx-sin2x*sinx)
=1/2[cosx*(1+cos2x)-2(sinx)^2*cosx]
=1/2[2*(cosx)^3-2(sinx)^2*cosx]
=cosx*[(cosx)^2-(sinx)^2]
=cosx*[2(cosx)^2-1]
=cosx*cos2x=左边
证明完毕

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