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