Question

We know that the cos 60 degrees = 1/2. Show that the above is true using a half angle identity.

Answer 1

$cos(x/2)=\sqrt{(1+cosx)/2}$

for $x=120^o$

$cos(120^{\circ}/2)=\sqrt{(1+cos120^o)/2}=\sqrt{(1-0.5)/2}=\sqrt{0.5/2}=\sqrt{1/4}=1/2$