sin2x-cos(2x+π/6)
=sin2x-(cos2xcosπ/6-sin2xsinπ/6)
=sin2x-(√3/2*cos2x-1/2*sin2x)
=3/2*sin2x-√3/2*cos2x
=√3*(√3/2*sin2x-1/2*cos2x)
=√3sin(2x-π/6)
sin2x-cos(2x+π/6)
=sin2x-(cos2xcosπ/6-sin2xsinπ/6)
=sin2x-(√3/2*cos2x-1/2*sin2x)
=3/2*sin2x-√3/2*cos2x
=√3*(√3/2*sin2x-1/2*cos2x)
=√3sin(2x-π/6)