已知向量a=(sinx,√3),b=(2cosx,cos2x),函数f(x)=ab,求f(x)的解析式和它的单调减区间

f(x)=ab=(sinx,√3）.(2cosx,cos2x)
=2sinxcosx+√3cos2x
=sin2x+√3cos2x
=2sin(2x+π/3)
它的单调减区间
2kπ+π/2≤2x+π/3≤2kπ+3π/2
即kπ+π/12≤x≤kπ+7π/12 (k∈Z)