Răspuns:
Explicație pas cu pas:
[tex]f(x)=\dfrac{\sin^4x+\cos^4x-1}{\sin^6x+\cos^6x-1}=\dfrac{(1-\cos^2x)^2+\cos^4x-1}{(1-\cos^2x)^3+\cos^6x-1}=\\\\=\dfrac{1-2\cos^x+\cos^4x+\cos^4x-1}{1-3\cos^2x+3\cos^4x-\cos^6x+\cos^6x-1}=\\\\=\dfrac{2\cos^4x-2\cos^2x}{3\cos^4x-3\cos^2x}=\dfrac{2(\cos^4x-\cos^2x)}{3(\cos^4x-\cos^2x)}=\boxed{\dfrac{2}{3}}[/tex]
