sina+sin^2a=1即cos^2a=sina
cos^2α+cos^6α+cos^8α
=sina+sin^3a+sin^4a
= sina+sin^2a+sin^3a+sin^4a-sin^2a
=1+sin^3a+sin^2a(sin^2a-1)
=1+sin^3a+sin^2a(-sina)
=1