左边= sin^6α+cos^6α
=( sin^2α+cos^2α)( sin^4α- sin^2αcos^2α+cos^4α)
= sin^4α- sin^2αcos^2α+cos^4α
= sin^4α+2sin^2αcos^2α+cos^4α-3sin^2αcos^2α
=(sin^2α+cos^2α)²-3sin^2αcos^2α
=1--3sin^2αcos^2α
=（1/cos²α- 3sin²α）/(1/cos²α)
=（(sin^2α+cos^2α)/cos²α- 3sin²α）/((sin^2α+cos^2α)/cos²α)
=(tan^2α+1-3sin^2α)/(tan^2α+1)=右边