8.
[TEX]cos^{4}x-cos2x+2sin^{6}x=0[/TEX]
=> [TEX]cos^{4}x-1+2sin^{2}x+2sin^{6}x=0[/TEX]
=> [TEX](cos^{2}x-1)(cos^{2}x+1)+2sin^{2}x+2sin^{6}x=0[/TEX]
=> [TEX]-sin^{2}x(cos^{2}x+1)+2sin^{2}x+2sin^{6}x=0[/TEX]
=> [TEX]sin^{2}x(cos^{2}x+1-2-2sin^{4}x)=0[/TEX]
=> [TEX]sin^{2}x(cos^{2}x-1-2sin^{4}x)=0[/TEX]
=> [TEX]sin^{2}x(-sin^{2}x-2sin^{4}x)=0[/TEX]
=> [TEX]sin^{4}x(2sin^{2}x+1)=0[/TEX]
........