化简变形f(x)=[2sin(x+π/3)+sinx]cosx-√3sin^2x

来源：学生作业帮助网编辑：作业帮时间：2024/04/30 04:10:08

化简变形f(x)=[2sin(x+π/3)+sinx]cosx-√3sin^2x
化简变形f(x)=[2sin(x+π/3)+sinx]cosx-√3sin^2x

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)

f(x) = (sin x + √3cos x + sin x)cos x - √3sin^2(x)
= 2sin x *cos x +√3（cos^2(x) - sin^2(x))
=sin(2x) + √3cos(2x)

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