1、f(0)=2,f(π/3)=1/2+√3/2.
代入函数(x)=（2acos^2x）+bsinxcosx求得a=1,b=2
f（x）=2cos²x+2sinxcosx
=sin2x+cos2x+1
=√2sin(2x+π/4)+1
函数的最小值=- 根号2,最大值=根号2
2、f(a)=0,a属于（0,2π）,
f（a）=√2sin(2a+π/4)+1=0
sin(2a+π/4)=-根号2/2
2a+π/4=π-π/4或2π+π-π/4
a=π/4或5π/4