将两个正弦展开后合并得：
f(x)=2sinxcosπ/6+(1+cosx)+a
=根号3sinx+cosx+(a+1)=2sin(x+π/6)+(a+1) (引入辅助角）
f(x)=2sin(x+π/6)+(a+1) 周期T=2π
(2) -π/3≤x+π/6≤2π/3
当x+π/6=π/2 时sin(x+π/2）取最大值 "1",所以f(x)(MAX)=2+(a+1)=(a+3)
当x+π/6= - π/3 时sin(x+π/2）取最小值：“-根号3/2”所以f(x)(min)= -根号3+（a+1)
f(x)(MAX)+f(x)(min)= -根号3+2*(a+1)=根号3 2*(a+1)= 2*根号3
a=根号3-1