(1)
f(x)＝cos²(x＋π/12)＝1/2[1＋cos(2x＋π/6)]
∵x＝x0是函數(shù)y＝f(x)圖像的一條對稱軸
∴2x0＋π/6＝kπ
即2x0＝kπ－π/6(k∈Z)
∴g(x0)＝1＋1/2sin2x0＝1＋1/2sin(kπ－π/6)
當k為偶數(shù)時,g(x0)＝1＋1/2sin(－π/6)＝1－1/4＝3/4
當k為奇數(shù)時,g(x0)＝1＋1/2sin(π/6)＝1＋1/4＝5/4
(2)
h(x)＝f(x)＋g(x)
＝1/2[1＋cos(2x＋π/6)]＋1＋1/2sin2x
＝1/2[cos(2x＋π/6)＋sin2x]＋3/2
＝1/2(√3/2•cos2x＋1/2sin2x)＋3/2
＝1/2sin(2x＋π/3)＋3/2
當2kπ－π/2 ≤ 2x＋π/3 ≤2kπ＋π/2
即kπ－5π/12 ≤ x ≤kπ＋π/12(k∈Z)時
函數(shù)h(x)＝1/2sin(2x＋π/3)＋3/2是增函數(shù)
故函數(shù)h(x)的單調(diào)增區(qū)間是[kπ－5π/12,kπ＋π/12](k∈Z)