Răspuns:
[tex]cos^2(x-x^2)+cos^2(x^2)-2cosx*cos(x^2)*cos(x-x^2)+cos^2x[/tex]
[tex]cos^2(x-x^2)+cos^2(x^2)-(cos(x+x^2)+cos(x-x^2))*cos(x-x^2)+cos^2x[/tex]
(Obs: Am transformat [tex]2cos(x)*cos(x^2)=cos(x+x^2)+cos(x-x^2)[/tex])
[tex]cos^2(x-x^2)+cos^2(x^2)-cos^2(x-x^2)-cos(x-x^2)*cos(x+x^2)+cos^2x[/tex]
[tex]cos^2(x^2)+cos^2x-cos(x-x^2)*cos(x+x^2)[/tex]
[tex]cos^2(x^2)+cos^2x-\frac{cos(x-x^2+x+x^2)+cos(x-x^2-x-x^2)}{2}[/tex]
(Obs: Am transformat produsul in suma)
[tex]\frac{2cos^2(x^2)+2cos^2x-cos(2x)-cos(2x^2)}{2}[/tex]
(Obs: Am adus la acelasi numitor)
[tex]\frac{2cos^2(x^2)+2cos^2x-cos^2x+sin^2x-cos^2(x^2)+sin^2(x^2)}{2}[/tex]
[tex]\frac{sin^2x+cos^2x+sin^2(x^2)+cos^2(x^2)}{2}[/tex]
[tex]\frac{1+1}{2}=\frac{2}{2}=1[/tex] => Expresia nu depinde de x
