Question

(1\3 · sin² 120°) -cos²120° cat faceee?

Answer 1

sin120=sin60=√3/2
cos120=-cos60=-1/2
Deci
1/3 * 3/4 - 1/4 = 0

Answer 2

   
[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]