sin^6α+cos^6α+3sin^2α*cos^2α
=(sin^2α+cos^2α)(sin^4α-sin^2α*cos^2α+cos^4α)+3sin^2α*cos^2α
=sin^4α+2sin^2α*cos^2α+cos^4α
=(sin^2α+cos^2α)^2
=1