几道高中函数题1.函数f（x）=sin（x+π/3）+asin（x-π/6）【a＞0】的一条对称轴方程为x=π/2,则a等于A.1 B.根号3 C.2 D.32.若1-tanA/1+tanA=2+根号3,则cot（45°+A）等于A.-2-根号3 B.-2+根号3 C.2+根号3 D.2-根号3

1、
f(x)=sin(x+π/3)-asin(π/6-x)
=sin(x+π/3)-acos[π/2-(π/6-x)]
=sin(x+π/3)-acos(x+π/3)
=√(a²+1)sin(x+π/3-b)
tanb=a/1=a
sinx对称轴x=kπ+π/2
所以x+π/3-b=kπ+π/2
这里x=π/2
b=-kπ+π/3
tanb=a=tan(π/3)=√3
选B
2、
(1-tanA)/(1+tanA)=2+√3
(1+tanA)/(1-tanA)=2-√3
(tanπ/4+tanA)/(1-tanπ/4tanA)=2-√3
tan(π/4+A)=2-√3
cot(π/4+A)=1/tan(π/4+A)=2+√3
选C