已知f(x)=cos^2x-sin^x+2sinxcosx.①求函数最小正周期②当x∈【0,π/2】时,求函数f(X)的最大值和最小值
问题描述:
已知f(x)=cos^2x-sin^x+2sinxcosx.①求函数最小正周期②当x∈【0,π/2】时,求函数f(X)的最大值和最小值
答
f(x)=cos^2x-sin^x+2sinxcosx= cos2x+sin2x= √2(sinπ/4cos2x+cosπ/4sin2x)= √2sin(2x+π/4)函数最小正周期 = 2π/2 = πx∈【0,π/2】2x∈【0,π】2x+π/4∈【π/4,5π/4】2x+π/4∈【π/4,π/2】时单调增2x+...