cos^8 x-sin^8 x=（cos^4 x-sin^4 x）（cos^4 x+sin^4 x）
cos^4 x-sin^4 x=(cos^2 x-sin^2 x)(cos^2x+sin^2 x)=cos2x
cos^4 x+sin^4 x=(cos^2x+sin^2 x)^2-2cos^2x*sin^2 x=1-(sin2x)^2/2
所以cos^8 x-sin^8 x=cos2x-cos2x(sin2x)^2/2=cos2x-(sin4xsin2x)/4
所以1/4sin2x*sin4x-sin^8 x+cos^8 x=1/4sin2x*sin4x+cos2x-(sin2xsin4x)/4=cos2x