16.复合函数单调性同增异减,即求cosx单减区间,x∈[2kπ,π+2kπ],k∈Z
17.也是复合函数.(1)-π+2kπ≤2x-π/4≤2kπ,x∈[-3π/8+kπ,π/8+2kπ],k∈Z
(2)π/2+2kπ≤π/6-2x≤3π/2+2kπ,x∈[-2π/3+kπ,-π/6+kπ],k∈Z
18.f(x)=a(1-cos2x)-√3asin2x+b用一下辅助角公式,
=a+b-2asin(2x+π/6)
∴当x=π/6时,f(x)min=a+b-2a=-5
x=π/2时,f(x)max=a+b+a=4
解得a=3,b=-2