f（x）=cos（2x-π/3）+2sin（x-π/4）sin（x+π/4）,x∈R.这个怎么配方啊?就是全部化成sin或cos、谢谢

f（x）=cos（2x-π/3）+2sin（x-π/4）sin（x+π/4）,x∈R.这个怎么配方啊?就是全部化成sin或cos、谢谢
f（x）=cos（2x-π/3）+2sin（x-π/4）sin（x+π/4）,x∈R.这个怎么配方啊?就是全部化成sin或cos、谢谢

f（x）=cos（2x-π/3）+2sin（x-π/4）sin（x+π/4）,x∈R.这个怎么配方啊?就是全部化成sin或cos、谢谢
f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
f(x)=1/2cos 2x+√3/2sin 2x+2(sin x-cos x)(xin x+cos x)
=1/2cos 2x+√3/2sin 2x-2(cos^2 x-sin^2 x)
=1/2cos 2x+√3/2sin 2x-2cos 2x
=-3/2cos 2x+√3/2sin 2x
=√3(1/2sin 2x-√3/2cos 2x)
=√3sin(2x-π/3)

sin(x-y)sin(x+y)=(sinxcosy-cosxsiny)(sinxcosy+cosxsiny)=sinxsinx-sinysiny=sin^2x-sin^2y
则
f（x）=cos（2x-π/3）+2sin（x-π/4）sin（x+π/4）
=cos2xcosπ/3+sin2xsinπ/3+2(sin^2x-sin^2*π/4)
=(0.5√3-1)...

全部展开

sin(x-y)sin(x+y)=(sinxcosy-cosxsiny)(sinxcosy+cosxsiny)=sinxsinx-sinysiny=sin^2x-sin^2y
则
f（x）=cos（2x-π/3）+2sin（x-π/4）sin（x+π/4）
=cos2xcosπ/3+sin2xsinπ/3+2(sin^2x-sin^2*π/4)
=(0.5√3-1)sin2x+0.5cos2x
=-0.5(√6-√2)sin(2x-5π/12)
若全化为sin cos 在倒数第二歩使用
sin2x=2sinxcosx cos2x=1-2sinxsinx=2cosxcosx-1即可

收起

f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)