化简½sin²x[（1/tan二分之x）-tan二分之x]+二分之根号三倍cos2x

化简½sin²x[（1/tan二分之x）-tan二分之x]+二分之根号三倍cos2x
化简½sin²x[（1/tan二分之x）-tan二分之x]+二分之根号三倍cos2x

化简½sin²x[（1/tan二分之x）-tan二分之x]+二分之根号三倍cos2x
1/2*sin²x*[1/tan(x/2)-tan(x/2)]+√3/2*cos2x
=1/2*sin²x*[cos(x/2)/sin(x/2)-sin(x/2)/cos(x/2)]+√3/2*cos2x
=1/2*sin²x*[cos²(x/2)-sin²(x/2)]/[sin(x/2)cos(x/2)]+√3/2*cos2x
=sin²x*cosx/sinx+√3/2*cos2x
=1/2*sin2x+√3/2*cos2x
=sin2xcos(π/3)+cos2xsin(π/3)
=sin(2x+π/3)