Question

函数f(x)=4cos^2(x+α)+4根号3sin(x+α)cos(x+α)-2的图像关于原点对称,则实数α的最小正值

Answer 1

f(x)＝2[2cos²(x+α)－1]＋2√3[2sin(x+α)cos(x+α)]＝2cos[2(x+α)]＋2√3sin[2(x+α)]

＝4sin[2(x+α)＋π/6]

∵图像关于原点对称 ∴f(0)＝0 ∴sin(2α＋π/6)＝0

∴实数α的最小正值是5π/12