[分析]根据诱导公式得到f(x)最大值,即得到关于x0的关系式,代入 tan (4(x)_(0)-dfrac (2pi )(3)) 利用诱导公式即可.-|||-[详解] (x)=3sin (4x+dfrac (pi )(3))+4sin (4x-dfrac (pi )(6))=3sin (4x+dfrac (pi )(3))+4sin (-dfrac (pi )(2)+4x+dfrac (pi )(3))-|||-.therefore f(x)=3sin (4x+dfrac (pi )(3))-4cos (4x+dfrac (pi )(3)) --|||-.therefore f(x)=5sin (4x+dfrac (pi )(3)-varphi )(tan varphi =dfrac (4)(3)) 。-|||-therefore (f(x))_(max)=5-|||-forall xin R exists (x)_(0)in R (x)leqslant f((x)_(0))-|||-.therefore 4(x)_(0)+dfrac (pi )(3)-varphi =dfrac (pi )(2)+2kpi (kin Z)-|||-therefore tan (4x-dfrac (2pi )(3))=tan (-dfrac (pi )(2)+2kpi +4)=-dfrac (1)(tan varphi )=-dfrac (3)(4)-|||-故选:B.-|||-8.在 Delta ABC 中, overrightarrow (BC)=3overrightarrow (BD) .overrightarrow (CF)=2overrightarrow (FA) ,E是AB的中点,EF与AD交于点P,若 overrightarrow (AP)=moverrightarrow (AB)+noverrightarrow (AC)-|||-则 m+n= ()-|||-A. dfrac (3)(7) B. dfrac (4)(7) C. dfrac (6)(7) D.1