已知(sinα-cosα)/(sinα+cosα)=1/3,则cos^4(π/3+α)-cos^4(π/6-α)的值为答案好像是（3-4√3）/10

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已知(sinα-cosα)/(sinα+cosα)=1/3,则cos^4(π/3+α)-cos^4(π/6-α)的值为答案好像是（3-4√3）/10已知(sinα-cosα)/(sinα+cosα)=

已知(sinα-cosα)/(sinα+cosα)=1/3,则cos^4(π/3+α)-cos^4(π/6-α)的值为答案好像是（3-4√3）/10
已知(sinα-cosα)/(sinα+cosα)=1/3,则cos^4(π/3+α)-cos^4(π/6-α)的值为
答案好像是（3-4√3）/10

已知(sinα-cosα)/(sinα+cosα)=1/3,则cos^4(π/3+α)-cos^4(π/6-α)的值为答案好像是（3-4√3）/10
[cos^4(π/3+α)]-[cos(π/6-α)]^2=[cos(π/3+α)]^4-[sin(π/3+α)]^4=[cos(π/3+α)]^2-[sin(π/3+α)]^2
=cos(2π/3+2α)
(sinα-cosα)/(sinα+cosα)=1/3
(1-tanα)/(1+tanα)=1/3
(1-tanα)/(1+tanα)=2/(1+tanα)-1=1/3
1+tanα=3/2 tanα=1/2 (cosα)^2=1/[1+(tanα)^2]=4/5 cos2α=2(cosα)^2-1=3/5
sin2α=2sinαcosα=2*(1*2)/5=4/5
cos(2π/3+2α)=cos(2π/3)cos(2α)-sin(2π/3)sin(2α)=(-3/10)-(4√3/10)

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