化简sin(2x+π/3)-(根号3)sin²x+sinxcosx+(根号3)/2

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化简sin(2x+π/3)-(根号3)sin²x+sinxcosx+(根号3)/2化简sin(2x+π/3)-(根号3)sin²x+sinxcosx+(根号3)/2化简sin(2x

化简sin(2x+π/3)-(根号3)sin²x+sinxcosx+(根号3)/2
化简sin(2x+π/3)-(根号3)sin²x+sinxcosx+(根号3)/2

化简sin(2x+π/3)-(根号3)sin²x+sinxcosx+(根号3)/2
∵√3/2-√3sin²x+sinxcosx=(√3/2)(1-2sin²x)+(1/2)sin2x
=sin(π/3)cos2x+cos(π/3)sin2x
=sin(2x+π/3),
∴原式=sin(2x+π/3)+(√3/2-√3sin²x+sinxcosx)
=2sin(2x+π/3).