化简变形f(x)=[2sin(x+π/3)+sinx]cosx-√3sin^2x
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/17 12:25:35
化简变形f(x)=[2sin(x+π/3)+sinx]cosx-√3sin^2x
=[2 sinx cosπ/3 +2cosx sinπ/3+sinx ]cosx-√3sin^2x
=[sinx+√3cosx+sinx]cosx-√3sin^2 x
=2sinxcosx+√3(cos^2x-sin^2x)
=sin 2x +√3cos 2x
=2(sin2x cosπ/3+ cos 2x sin π/3)
=2sin(2x+π/3)
=[sinx+√3cosx+sinx]cosx-√3sin^2 x
=2sinxcosx+√3(cos^2x-sin^2x)
=sin 2x +√3cos 2x
=2(sin2x cosπ/3+ cos 2x sin π/3)
=2sin(2x+π/3)
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