Answer:
See explanation and proof below.
Step-by-step explanation:
For this case we want to proof this identity:
[tex] cos(\frac{\theta}{2}) = \pm \sqrt{\frac{1+ cos(x)}{2}}[/tex]
And we need to us the double angle formula given by:
[tex] cos^2 (x) = \frac{1+ cos (2x)}{2}[/tex]
If we use a substitution for example [tex] x = \frac{\theta}{2}[/tex] we see that the double angle formila is given by:
[tex] cos^2(\frac{\theta}{2}) = \frac{1+ cos (2\frac{\theta}{2})}{2}[/tex]
And we got:
[tex] cos^2(\frac{\theta}{2}) = \frac{1+ cos (\theta)}{2}[/tex]
And if we apply sqaure root on both sides we got:
[tex] cos(\frac{\theta}{2}) = \pm \sqrt{\frac{1+ cos (\theta)}{2}}[/tex]
And that complete the proof
