Докажите,что верно равенство:sin^2x+sin^4x+cos^2x-cos^4x=1-cos2x

[latex]sin^2x+sin^4x+cos^2x-cos^4x=1-cos2x[/latex] [latex]cos^2x-cos^4x+1-cos^2x+sin^4x=1-cos2x[/latex] [latex]cos^2x-cos^4x+1-cos^2x+(1-cos^2x)^2=1-cos2x[/latex] [latex]cos^2x-cos^4x+1-cos^2x+1-2cos^2x+cos^4x=1-cos2x[/latex] [latex]2-2cos^2x=1-cos2x[/latex] [latex]2-2cos^2x=1-2cos^2x-1[/latex] [latex]2-2cos^2x=2-2cos^2x[/latex]                                                    ч.т.д