F(x)=2cos(π/6-2x)+ 3cos under the radical sign? X+sinxcosx- 3 under radical sign
= sin2x/2 under the radical sign+3cos2x/2+2cos-3/2 under the radical sign.
= sin2x/2 under the root number+3cos2x/2+3cos2x under the root number+sin2x-3 under the root number.
=3sin(2x+π/3)- 3 under the radical sign
Minimum positive period =2π÷2=π
When 2x+π/3=2kπ+π/2
That is, when x=kπ+π/ 12, there is a maximum value =3- 3 under the root sign.
Decreasing interval:
2kπ+π/2 & lt； = 2x+π/3 & lt； =2kπ+3π/2
kπ+π/ 12 & lt； = x & lt=kπ+7π/ 12