化简：f（x）=2cosx(sinx-√3cosx)+√3

题目

化简：f（x）=2cosx(sinx-√3cosx)+√3

答案

f(x)=2sinxcosx-2√3cos²x+√3
=sin2x-2√3(1+cos2x)/2+√3
=sin2x-√3cos2x
=2(sin2x*1/2-cos2x*√3/2)
=2(sin2xcosπ/3-cos2sinπ/3)
=2sin(2x-π/3)