Question

calculati cos2 120+sin2 60

Answer 1

 

$\displaystyle\\\cos120^o=\cos(180^o-60^o)=-\cos60^o\\\\\cos^2120^o+sin^260^o=\\\\=\Big(\cos120^o\Big)^2+sin^260^o=\\\\=\Big(-\cos60^o\Big)^2+sin^260^o=\\\\=\left(-\frac{1}{2}\right)^2+\left(\frac{\sqrt{3}}{2}\right)^2=\\\\\\ =\frac{1}{4}+\frac{3}{4}=\frac{1+3}{4}=\frac{4}{4}=\boxed{\bf1}$