Răspuns:
[tex]cos^2x+cos^2y+cos^2z-2cosx*cosy*cosz=1[/tex]
[tex]cos^2x+cos^2y+cos^2z-(cos(x+y)+cos(x-y))*cosz=1[/tex]
[tex]cos^2x+cos^2y+cos^2z-cos^2z-cos(x-y)*cos(x+y)=1[/tex]
[tex]cos^2x+cos^2y-\frac{cos(x-y+x+y)+cos(x-y-x-y)}{2}=1[/tex]
[tex]\frac{2cos^2x+2cos^2y-cos(2x)-cos(2y)}{2}=1[/tex]
[tex]\frac{2cos^2x+2cos^y-cos^2x+sin^2x-cos^2y+sin^2y}{2}=1[/tex]
[tex]\frac{sin^2x+cos^2x+sin^2y+cos^2y}{2}=1[/tex]
[tex]\frac{1+1}{2}=\frac{2}{2}=1[/tex] c.c.t.d.
