1、f(x)=ab
=1/2*cos2x+√3/2*sin2x
=sin(π/6)cos2x+cos(π/6)sin2x
=sin(2x+π/6)
∵-1≤sin2(x+π/12)≤1
∴函数值域为：[-1,1]
函数的单调增区域为：
-π/2+2kπ≤2x+π/6π/2+2kπ,k∈Z
即-π/3+kπ≤x≤π/6+kπ,k∈Z
则函数的单调增区间为：[-π/3+kπ,π/6+kπ],k∈Z
2、函数图像由y=sinx先向左平移π/6个单位,再保持纵坐标不变、横坐标变为为原来的1/2变换得到的.