已知 f(x)=sin(2x+π/6)+cos(2x-π/3) ,求f(x)的最大值及取得最大值时X的值.

f(x)=sin(2x+π/6)+cos(2x-π/3)
=sin(2x)cos(π/6)+cos(2x)sin(π/6)+cos(2x)cos(π/3)+sin(2x)sin(π/3)
=sin(2x)[cos(π/6)+sin(π/3)]+cos(2x)[sin(π/6)+cos(π/3)]
=2sin(2x)cos(π/6)+2cos(2x)sin(π/6)
=2sin(2x+π/6)