函数f（x）等于sinxcosx（x-4分之pai）+sin（2分之pai+x）sin（x-4分之p
问题描述：
函数f（x）等于sinxcosx（x-4分之pai）+sin（2分之pai+x）sin（x-4分之p
ai）的图像关于什么对称（答案是x=8 分之3pai）
答
f(x)=sinxcos(x-π/4)+sin(π/2+x)sin(x-π/4)
=sinx(cosxcosπ/4+sinxsinπ/4)+cosx(sinxcosπ/4-cosxsinπ/4)
=sinx[(√2/2)cosx+(√2/2)sinx]+cosx[(√2/2)sinx-(√2/2)cosx]
=√2sinxcosx-(√2/2)[(cosx)^2-(sinx)^2]
=(√2/2)sin2x-(√2/2)cos2x
=sin2xcosπ/4-cos2xsinπ/4
=sin(2x-π/4)
2x-π/4=kπ+π/2,则对称轴为x=kπ/2+3π/8
当k=0时,对称轴为x=3π/8
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