Can someone explain to me how cos(theta/2) can be recongfigured into The square root of (1/2+ cos(theta)/2). Thanks.
We can use the double angle formula to get it:
$\displaystyle \cos \theta = \cos \left(2 \cdot \frac {\theta}{2} \right)$
$\displaystyle = \cos^2 \left( \frac {\theta}{2} \right) - \sin^2 \left( \frac {\theta}{2} \right)$
$\displaystyle = \cos^2 \left( \frac {\theta}{2} \right) - \left[ 1 - \cos^2 \left( \frac {\theta}{2} \right) \right]$
$\displaystyle = 2 \cos^2 \left( \frac {\theta}{2} \right) - 1$
So we have: $\displaystyle \cos \theta = 2 \cos^2 \left( \frac {\theta}{2} \right) - 1$
solving for $\displaystyle \cos \left( \frac {\theta}{2} \right)$ we obtain the desired result