A.Maths Trigonometry

sin²x=1-sinx
1-cos²x=1-sinx
cos²x=sinx
∴cos^4x=sin²x
∴cos^4x+cos²x-1=sin²x+sinx+1=0

From (a), cos²x-1=-cos^4x
∴cos^8x+cos^6x+cos²x-1=cos^8x+cos^6x-cos^4x
=cos^4x(cos^4x+cos²x-1)
=cos^4x(0)(From (a))
=0

sinθ+sinθ-1=0
sinθ=1-sinθ
1-sinθ=sinθ
cosθ=sinθ

cos4θ + cosθ - 1
=(cosθ)+cosθ-1
=sinθ+sinθ-1
=0

cos8θ + cos6θ + cosθ - 1
=(cosθ)4+(cosθ)+cosθ-1
=sin4θ+sinθ+sinθ-1
=sin4θ+sinθ-sinθ
=sinθ(sinθ+sinθ-1)
=0