f(x)=3√3sinxcosx＋2cos²x＋(sin²x＋2cos²x)－(5/2)
=(3√3/2)sin2x＋(3/2)(cos2x＋1)－(3/2)
=3[(√3/2)sin2x＋(1/2)cos2x]
=3sin(2x＋π/6)
1、x∈[π/6,π/2]
则：2x＋π/6∈[π/2,7π/6]
则：f(x)∈[－3/2,3]
2、f(a)=3sin(2a＋π/6)=3,则：a=π/6,则：f(a－π/12)=f(π/12)=3sin(π/3)=3√3/2第二问错了2、f(a)=3sin(2a＋π/6)=3，则：a=π/6，则：f(a－π/12)=f(π/6－π/12)=f(π/12)=3sin[2×(π/12)＋π/6]=3sin(π/3)=3√3/2