已知函数fx=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)告诉我这个式子怎么化简就好了,我写到1/2cos2x+√3/2sin2x+sin2x就不知道怎么算了
问题描述：
已知函数fx=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
告诉我这个式子怎么化简就好了,我写到1/2cos2x+√3/2sin2x+sin2x就不知道怎么算了
答
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(2x-π/2)=cos2x*(1/2)+si...