已知函数f（x）=√3sinxcosx-1/2cos∧2x+1/2sin∧2x-1
问题描述：
已知函数f（x）=√3sinxcosx-1/2cos∧2x+1/2sin∧2x-1
（1）当x∈[0,π/2]时,求函数f（x）的最小值和最大值
（2）设△ABC的内角A,B,C的对边分别为a,b,c,且c=√3f（C）=0 若向量m=（1,sinA）与向量n=（2,sinB）共线 求a,b的值
谢谢
答
cos^2 x = (1+cos2x)/2
sin^2 x = (1-cos2x)/2
f(x) = sqrt(3)/2 sin2x - (1 + cos2x)/4 + (1 - cos2x)/4- 1 = sqrt(3)/2 sin2x - 1/2 cos2x - 1
= sin(2x - pi/6) - 1
(1) 最大值0,最小sin(-pi/6) - 1 = -1.5
(2) f(C) = 0, 2C-pi/6 = pi/2, C = pi/3
sinA/1 = sinB/2
sinB = 2sinA
a/sinA = c/sinC = 2
a = 2sinA
b = 2sinB = 4sinA
b = 2a
a = 1, b = 2, c = sqrt(3)