已知sin(α+β)sin(α-β)=1/3

sin(α+β)sin(α-β)
=(sinαcosβ+sinβcosα)(sinαcosβ-sinβcosα)
=sin^2αcos^2β-sin^2βcos^2α
=sin^2α(1-sin^2β)-sin^2β(1-sin^2α)
=sin^2α-sin^2β
=1/3
1. cos2β-cos2α=1-2sin^2β-1+2sin^2α
=2(sin^2α-sin^2β)
=2/3
2.1/4(sin2a)^2+(sinβ)^2+(cosα)^4 (是这个吗？原式算不出来哎~~）
=sin^2α*cos^2α+sin^2β+cos^4α
=cos^2α(sin^2α+cos^2α)+sin^2β
=cos^2α+sin^2β
=1-(sin^2α-sin^2β)
=1-1/3
=2/3

cos2β-cos2α
= 2cosβ^2-1 - (2cosα^2-1)
= 2 (cosβ^2 - cosα^2)
=2(cosβ + cosα)(cosβ - cosα)
= 8 cos(β+α)/2cos(β-α)/2 sin(β+α)/2sin(β-α)/2
= 2 sin(β+α)sin(β-α)
= 2/3