急求答案 已知 函数f(x) =2√3sin2x+[(cos3x)/(cosx)]求函数f(x)的最大值及...

f(x) =2√3sin2x+[(cos3x)/(cosx）]
∵cos3x=cos(2x+x)
=cos2xcosx-sin2xsinx
=cos2xcosx-2sin²xcosx
∴f(x) =2√3sin2x+[(cos3x)/(cosx）]
=2√3sin2x+cos2x-2sin²x
=2√3sin2x+cos2x-1+cos2x
=2√3sin2x+2cos2x-1
=4sin(2x+π/6)-1
( cosx≠0,x≠kπ+π/2,k∈Z
2x≠2kπ+π,k∈Z
2x+π/6≠kπ+7π/6,k∈Z)
∴ 当 2x+π/6=2kπ+π/2,k∈Z
即 x=kπ+π/6,k∈Z时,f(x) 取得最大值3