Answer:
Half angle Identity for cosine:
[tex]$\cos \left(\frac{\theta}{2} \right)=\pm \sqrt{\frac{1+\cos(\theta)}{2} } $[/tex]
[tex]\text{Note that it is} \pm \text{because we don't know which Quadrant the half-angle is, }[/tex][tex]\text{the information of}\cos(\theta) \text{is not enough to conclude the angle}[/tex]
[tex]$\frac{\pi}{8} \text{ is a Quadrant I angle, therefore, positive}$[/tex]
[tex]$\cos \left(\frac{\pi}{8} \right)=\sqrt{\frac{1+\cos(\frac{\pi}{4} )}{2} } $[/tex]
The equation is true.
