f(x)=(2cosx,cosx)·(cosx,2sinx)=2cos²x+2sinxcosx=cos2x+sin2x+1
=2½(cos2xsinπ/4+sin2xcosπ/4)+1=2½sin(2x+π/4)+1
单调增加：2kπ-π/2≤2x+π/4≤2kπ+π/2,即：kπ-3π/8≤x≤kπ+π/8
单调减少：2kπ+π/2≤2x+π/4≤2kπ+3π/2,即：kπ+π/8≤x≤kπ+5π/8
单调增区间：[kπ-3π/8,kπ+π/8];
单调减区间：[kπ+π/8,kπ+5π/8].
注：2½表示根号2