三角函数小题~谢啦!http://hi.baidu.com/%BA%AF%CA%FD%C8%FD%BD%C7%CE%D2

(1)
由于:
f(x)
=cos(3x/2)cos(x/2)-sin(3x/2)sin(x/2)
+2根号3*sinxcosx
=[cos(3x/2)cos(x/2)-sin(3x/2)sin(x/2)]
+根号3*(2sinxcosx)
=cos[(3x/2)+(x/2)]+根号3*sin2x
=cos2x+根号3sin2x
=2sin(2x+pi/6)
则:
f(pi/12)
=2sin(2pi/12+pi/6)
=2sin(pi/3)
=根号3
(2)
由于sin(2x+pi/6)属于[-1,1]
则:当sin(2x+pi/6)=1时,
f(x)取最大值=2
此时:
2X+pi/6=pi/2+2kpi
则:{X|X=pi/6+kpi,k属于Z}
f(x)最大值为2