已知f(x)=2sin(x+π/6)cos(x+π/6),g(x)=1-2sin^2(x+π/12),要得到函数g(x)的图像，只需把函数f(x)图像

A.向左平移π/6个单位长度
B.向右平移π/6个单位长度
C.向左平移π/3个单位长度
D.向右平移π/3个单位长度

结论:A
理由:f(x)=sin(2(x+π/6))=sin(2x+π/3)
,g(x)=cos(2(x+π/12))=cos(2x+π/6)
=sin((2x+π/6)+π/2)=sin(2(x+π/6)+π/3)
即g(x)=sin(2(x+π/6)+π/3)
只需用x+π/6替换f(x)=sin(2x+π/3)中的x即可得到g(x).
即只需把函数f(x)图像向左平移π/6个单位长度
所以 选A.

(1)∵cos2x=2cos^2x-1 ∴f(x)=1/2+cos(2x+π/6)/2 对称轴2x0+π/6=π+2kπ x0=5π/12+kπ g(x0)=1+1/2sin(5π/6+2kπ)=5/4 （2）h(x)=1/2+cos(2x+π/6)/2+1+1/2sin2x =3/2+0.5*(√3/2*cos2x-1/2sin2x+sin2x) =3/2+0.5*sin(2x+π/3) 递减区间（π/12+kπ,7π/12+kπ）