f(x)=根号3*sinwx+cos(wx+π/3)+cos(wx-π/3)且f(x)最小正周期为π/2这当0

Question

f(x)=根号3*sinwx+cos(wx+π/3)+cos(wx-π/3)且f(x)最小正周期为π/2这当0

Answer 1

f(x)=√3*sinwx+coswxcosπ/3-sinwxsinπ/3+coswxcosπ/3+sinwxsinπ/3
=√3*sinwx+2coswxcosπ/3
=√3*sinwx+coswx
=2sin(wx+30`)
w=4
0<=x<=π/2,4x+30`∈[30`,390`]
4x+30`∈[90`,270`]
减区间：[15`,60`]