f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4) 求最小正周期和图像的对称轴方程,

问题描述:

f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4) 求最小正周期和图像的对称轴方程,

f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)= cos2x cosπ/3+ sin2x sinπ/3+2sin(x-π/4)cos(π/4-x)= cos2x cosπ/3+ sin2x sinπ/3+2sin(x-π/4)cos(x-π/4)= cos2x cosπ/3+ sin2x sinπ/3+ sin...为什么2sin(x-π/4)cos(x-π/4)直接变成 sin(2x-π/2)?这是二倍角正弦公式2sinacosa=sin2a.这里a=x-π/4,2sin(x-π/4)cos(x-π/4)=sin[2(x-π/4)]=sin(2x-π/2)