已知函数f(x)＝cos^2wx-sin^2wx＋2√3coswxsinwx,其中w＞0,若y＝f(x)的图像相邻两对称

已知函数f(x)＝cos^2wx-sin^2wx＋2√3coswxsinwx,其中w＞0,若y＝f(x)的图像相邻两对称轴的距离大于等于π/2(1)求w的取值范围 (2)在△ABC中,abc分别是角ABC的对边,a＝√3,b＋c＝3,当w取得最大值时,f(A)＝1,求△ABC的面积
(1)解析：∵函数f(x)＝cos^2wx-sin^2wx＋2√3coswxsinwx,其中w＞0
f(x)=cos2wx+√3sin2wx
=2sin(2wx+π/6)
∵f(x)的图像相邻两对称轴的距离大于等于π/2
∴T/2>=π/2==>T>=π==>2π/2w>=π==>0

f(x) = cos2wx + sqrt(3) sin2wx
= 2 sin(2wx + pi/6)
the period of this function is 2pi/(2w) = pi/w
so w = 2
2. f(A) = 2sin(2wA+pi/6) = 1, 4A+pi/6 = 5pi/6
A = pi/6搜索
when b=c, b+c is maximum
b = sqrt(3)/sin15 = 2sqrt(3) / sqrt(2-sqrt(3))
period:周期
function: 函数
maximum:极大值