已知函数f(x)=2cosxsin(x+π/3)-√3/2 1.求函数f(x)的最小正周期T 2.若△ABC的三边a,b,c满足b²=ac,且边b所对角为B,试求cosB的取值范围,并确定此时f(B)的最大值
问题描述:
已知函数f(x)=2cosxsin(x+π/3)-√3/2 1.求函数f(x)的最小正周期T 2.若△ABC的三边a,b,c
满足b²=ac,且边b所对角为B,试求cosB的取值范围,并确定此时f(B)的最大值
答
1. f(x)=2cosxsin(x+π/3)-√3/2 = 2cosx(sinx cosπ/3 + cosx sinπ/3 ) -√3/2 = cosx sinx + √3cos²x -√3/2 = 1/2 sin2x + √3/2 cos2x = sin(2x+π/3)所以 T = 2π/2...