已知sin^4a+cos^4a=5/9,兀

已知sin^4a+cos^4a=5/9,兀
已知sin^4a+cos^4a=5/9,兀

已知sin^4a+cos^4a=5/9,兀
tanα+cotα=sinα/cosα+cosα+sinα=(sin^2α+cos^2α)/cosαsinα=1/sinαcosα
=2/sin2α
sin^2α=(1-cos2α)/2 cos^2α=(1+cos2α)/2
sin^4α+cos^4α=[(1-cos2α)/2]^2+[(1+cos2α)/2]^2
=1/2+1/2*cos^2(2α)=5/9
cos^2(2α)=1/9 sin^2(2α)=1-cos^2(2α)=8/9
π