已知函数f(x)=2sinxcosx+sin(2x+π/2)+1 1.求他的最小正周期和最大值 2.求y=f(x)的单调区间

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已知函数f(x)=2sinxcosx+sin(2x+π/2)+1 1.求他的最小正周期和最大值 2.求y=f(x)的单调区间

f(x)=2sinxcosx+sin(2x+π/2)+1=sin2x+cos2x+2=√2sin(2x+π/4)+11.最小正周周期T=2π/2=π当sin(2x+π/4)=1时取最大值即当2x+π/4=2kπ+π/2,x=kπ+π/8时,y的最大值为√2+12.、单调增区间:2kπ-π/2 ≤2x+π/...