[tex]\displaystyle\\
\text{Folosim formulele:}\\
120^o = 180^o-60^o\\
\sin120^o = \sin(180^o - 60^o) = \sin60^o = \frac{ \sqrt{3} }{2} \\\\
\cos120^o = \cos(180^o - 60^o) = -\cos60^o = -\frac{ 1 }{2} \\\\
\text{Rezolvare:}\\\\
\frac{1}{3} \sin^2 120^o -\cos^2 120^o=\\\\
=\frac{1}{3} \sin^2( 180^o-60^o) -\cos^2 (180^o-60)=\\\\
=\frac{1}{3} \sin^2( 60^o) -(-\cos (60))^2=\\\\
=\frac{1}{3} \times \left(\frac{ \sqrt{3} }{2} \right)^2 - \left(-\frac{ 1 }{2} \right)^2 =
[/tex]
[tex]\displaystyle\\
=\frac{1}{3} \times \frac{3 }{4} - \frac{ 1 }{4} = \frac{ 1 }{4} - \frac{ 1 }{4} = \boxed{0}[/tex]
