已知f(x) = cos(2x - π/2) + 2sin(x - π/4)sin(x + π/4),求图像对称轴方程已知f(x) = cos(2x - π/2) + 2sin(x - π/4)sin(x + π/4),求图像对称轴方程

已知f(x) = cos(2x - π/2) + 2sin(x - π/4)sin(x + π/4),求图像对称轴方程
已知f(x) = cos(2x - π/2) + 2sin(x - π/4)sin(x + π/4),
求图像对称轴方程

f(x)=cos(π/2-2x)+2sin(x-π/4)cos(π/2-(x+π/4))
=sin2x+2sin(x-π/4)cos(π/4-x)
=sin2x+2sin(x-π/4)cos(x-π/4)
=sin2x+sin(2x-π/2)
=sin2x-sin(π/2-2x)
=sin2x-cos2x
=根号2*sin(2x-π/4)
故对称轴为x=3π/8+kπ/2,其中k是整数