S-I : If  $\overline{a}$  and $\overline{b}$  are two unit vectors then ${\left|\overline{a}+\overline{b}\right|}^2+{\left|\overline{a}-\overline{b}\right|}^2=4$ 
S-II : If $\overline{a}$   and $\overline{b}$  two unit vectors inclined at an angle $\theta$ . Then the unit  vectors along their sum and difference are  $\frac{\overline{a}+\overline{b}}{2\cos \left(\theta /2\right)}$ and  $\frac{\overline{a}-\overline{b}}{2\sin \left(\theta /2\right)}$ respectively
 

${\left|\overline{a}+\overline{b}\right|}^2+{\left|\overline{a}-\overline{b}\right|}^2=2\left({\left|\overline{a}\right|}^2+{\left|\overline{b}\right|}^2\right)$

So ,  S-I is true 
S-II :  Since,   $\overline{a},\overline{b}$ are unit vectors then 
${\left|\overline{a}+\overline{b}\right|}^2={\left|\overline{a}\right|}^2+{\left|\overline{b}\right|}^2+2\cos \left(\overline{a},\overline{b}\right)$ 
  = $1+1+2\cos \theta$ 
$=2\left(1+\text{Cos}\theta \right)=4{\cos }^2\left(\frac{\theta }{2}\right)$  
and  ${\left|\overline{a}-\overline{b}\right|}^2=4{\sin }^2\left(\frac{\theta }{2}\right)$  
$\therefore$  Unit vector along $\overline{a}+\overline{b}$  and $\overline{a}-\overline{b}$are $\frac{\overline{a}+\overline{b}}{2\cos \left(\theta /2\right)}$  and  $\frac{\overline{a}-\overline{b}}{2\sin \left(\theta /2\right)}$ respectively.
S-I is true, S-II is true, S-II is not correct explanation for S-I