已知函数f(x)=-√3sin²x+sinxcosx 化简

已知函数f(x)=-√3sin²x+sinxcosx 化简
已知函数f(x)=-√3sin²x+sinxcosx 化简

已知函数f(x)=-√3sin²x+sinxcosx 化简
f(x)=-√3sin²x+sinxcosx
=-√3(1-cos2x)/2+1/2*sin2x
=√3/2*cos2x+1/2*sin2x-√3/2
=cos2xcosπ/6+sin2xsinπ/6-√3/2
=cos(2x-π/6)-√3/2

f（x）= - 根号3sin2x+1/2sin2x

原式=－√3/2(1－cos2x)＋1/2sin2x
=sin60cos2x＋cos60sin2x－√3/2
=sin(60＋2x)－√3/2