If sin x +sin^2 x=1 then find the value of cos^8 x +2cos^6 x+cos^4 x(INDEX;^2 : means to the power of)

Sinx +sin²x=1
sinx=1-sin²x
sinx=cos²x
sin²x=cos⁴x
so,
cos^8x+2cos^6x+cos⁴x
=cos⁴x(cos⁴x+2cos²x+1)
=sin²x (sin²x+2sinx+1)
=sin⁴x+2sin³x+sin²x
=sin⁴x+sin³x+sin³x+sin²x
=sin²x(sin²x+sinx)+ sinx(sin²x+sinx)
=sin²x×(1)+ sinx(1)
=sin²x+sinx
= 1