Question

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

Answer 1

f(x)=cos(2x-π/腔链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)+sin2x*(√3/2)-cos2x
=(√3/2)*sin2x-(1/2)*cos2x
=sin(2x-π/6)

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