Question

ce trebuie facut pentru a demonstra ca o functie este constanta pe domeniul maxim de definitie.?

f(x)= sin ^4 x+ cos^4x -1 supra sin^6 x + cos ^6 x -1

Answer 1

Răspuns:

Explicație pas cu pas:

$f(x)=\dfrac{\sin^4x+\cos^4x-1}{\sin^6x+\cos^6x-1}=\dfrac{(1-\cos^2x)^2+\cos^4x-1}{(1-\cos^2x)^3+\cos^6x-1}=\\\\=\dfrac{1-2\cos^x+\cos^4x+\cos^4x-1}{1-3\cos^2x+3\cos^4x-\cos^6x+\cos^6x-1}=\\\\=\dfrac{2\cos^4x-2\cos^2x}{3\cos^4x-3\cos^2x}=\dfrac{2(\cos^4x-\cos^2x)}{3(\cos^4x-\cos^2x)}=\boxed{\dfrac{2}{3}}$