1.f(x)=(sinx)^2+2sinxcosx+3(cosx)^2=1+sin2x+2(cosx)^2=sin2x+cos2x+2=√2sin(2x+π/4)+2所以f(x)的最大值是2+√2当2x+π/4=2kπ+π/2(k∈Z),即x=kπ+π/8(k∈Z)时f(x)取的最大值所以取得最大值时的自变量x的集合...