упростить cos^6 α + sin^6 α+ 3cos^2 α * sin^2 α

Question

упростить

cos^6 α + sin^6 α+ 3cos^2 α * sin^2 α

Answer 1

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