1.f(x)=(cosx)^2-6cosx-2=(cosx-3)^2-11
考查g(x)=cosx和h(x)=(x-3)^2-11的单调性有：
k＜0时,[2kπ-π,2kπ]单减,[2kπ,2kπ+π]单增
k≥1时,[2kπ-π,2kπ]单增,[2kπ,2kπ+π]单减
k=0时,[0,3]单增,[3,π]、[-π,0]单减
2.f(x)=2(cosx)^2+√3sin2x+a
=1+cos2x+√3sin2x+a
=2sin(2x+π/6)+a+1
(1)单增区间：2kπ-π/2≤2x+π/6≤2kπ+π/2,即：[kπ-π/3,kπ+π/6]
单减区间：2kπ+π/2≤2x+π/6≤2kπ+3π/2,即：[kπ+π/6,kπ+2π/3]
(2)x∈[0,π/2],[0,π/6]单增,[π/6,π/2]单减,于是:x=π/6,f(x)最大,代入有：f(π/6)=3+a=4,于是：a=1