[tex]\sin^2x=1-\cos^2x\\
(a-b)^4=(a-b)^2(a-b)^2=a^4+b^4-4a^3b+6a^2b^2-4ab^3\\
E(x)=\sin^8x-\cos^8x+4\cos^6x-6\cos^4x+4\cos^2x=\\=(1-\cos^2x)^4-\cos^8x+4\cos^6x-6\cos^4x+4\cos^2x=\\=1+\cos^8x-4\cos^2x+6\cos^4x-4\cos^6x-\cos^8x+4\cos^6x\\-6\cos^4x+4\cos^2x=1.[/tex]