cos^6a+sin^6a=(cos^2a+sin^2a)*(cos^4a+sin^4a-cos^2asin^2a)=
=(cos^2a-sin^2a)^2+cos^2asin^2a=(cos2a)^2+1/4(sin2a)^2=
=cos4a+5/4sin^2(2a)=cos4a+5/4(1/2(1-cos4a))=cos4a+5/8-5/8cos4a=
=1/8(5+3cos4a)
cos^6a+sin^6a=(cos^2a+sin^2a)*(cos^4a+sin^4a-cos^2asin^2a)=
=(cos^2a-sin^2a)^2+cos^2asin^2a=(cos2a)^2+1/4(sin2a)^2=
=cos4a+5/4sin^2(2a)=cos4a+5/4(1/2(1-cos4a))=cos4a+5/8-5/8cos4a=
=1/8(5+3cos4a)