设f(x)=6cos²x-√3sin2x

cos2x = 2cos^2 x - 1
===>
6cos^2 x = 3cos2x + 3
f(x)= 3cos2x -√3sin2x + 3
=2√3( √3/2 cos2x - 1/2 sin2x ) + 3
=2√3cos(2x+TT/6)+3
最小正周期：2TT/2 =TT
若
2x+TT/6=TT/2 + 2kTT
,k (- Z
即
x=TT/6 + kTT
,k (- Z
f(x)最大值=3+2√3
若
2x+TT/6=-TT/2 + 2kTT
,k (- Z
即
x=-TT/3 + kTT
,k (- Z
f(x)最小值=3-2√3