f(x)=cos(2x-x/3)+2sin(x-π/4)sin(x+π/4)sin(x+π/4)化简.
问题描述：
f(x)=cos(2x-x/3)+2sin(x-π/4)sin(x+π/4)sin(x+π/4)
化简.
答
似乎是f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
=cos(2x-π/3)+2sin(x-π/4)cos[π/2-(x+π/4)]
=cos(2x-π/3)+2sin(x-π/4)cos(π/4-x)
=cos(2x-π/3)+2sin(x-π/4)cos(x-π/4)
=cos(2x-π/3)+sin[2(x-π/4)]
=cos2xcosπ/3+sin2xsinπ/3+sin(2x-π/2)
=cos2x*1/2+sin2xsinπ/3-cos2x
=sin2xsinπ/3-cos2x*1/2
=sin2xsinπ/3-cos2x*cosπ/3
=-cos(2x+π/3)