已知函数f(x)=Asin(2x+a),若函数f(x+π/6)为偶函数,且f(π/6)=4,求f(x)解析式

f(x+pai/6)=Asin(2x+pai/3+a)=Acos(pai/6-a-2x)pai/6-a=2kpai,pai/6-a=2kpai+paif(x)=Asin(2x+pai/6-2kpai)=Asin(2x+pai/6)f(pai/6)=Asinpai/2=A=4a=-7/6pai-2kpaif(x)=Asin(2x-7/6pai)f(pai/6)=Asin(-5/6pai)=-A/2=4A=-8f(x)=4sin(2x+pai/6)