True or false and why. I think it is false but I'm having trouble explaining it. cos α/2 =+/- square root of (1+cosα/2), where the + or - sign depends on the angle α/2.

Question

dumbcow · Answer

its actually true...its a half-angle identity

anonymous · Answer

what if alpha = 0 ?

anonymous · Answer

wait is it cos(x/2) or (cosx)/2

anonymous · Answer

what dumbcow said, it is correct assuming you mean 
$$\cos(\frac{\alpha}{2})=\pm\sqrt{\frac{1+\cos(\alpha)}{2}}$$

anonymous · Answer

yes that is correct

anonymous · Answer

yus that is true. sorry the lack of brackets confused me

anonymous · Answer

then it is  right
$\alpha =0$ poses no challenge to the formula, get 1 on both sides

dumbcow · Answer

the why comes from using double angle identity
$$\cos(2 \alpha) = 2\cos^{2} \alpha -1$$
solve for cos(alpha) and you obtain the half angle identity