Question

cos(a/2) = + or - sqrt(1 + cos a / 2 ) for all values of a. True or false?

Answer 1

write it this way:
cos(a/2)^2=(1+cos a)/2
then:
2 cos^2(a/2)=(1+cos a)
now:
cos a = cos^2(a/2)-sin^2(a/2) and 1 =sin^2(a/2) +cos^2(a/2)
so:
1+cos a = sin^2(a/2) +cos^2(a/2) + cos^2(a/2)-sin^2(a/2) =2cos^2(a/2)
so it is true

Answer 2

@Spectrum