Help please: trig identities with ?

Question

So i figured out other problems somewhat similar to these two but still majorly confused. Help would be greatly appreciated :)

you have to use other trig identities to prove these two statements are true. I guess the roots throw me off. guidance in any way would be so wonderful!

absolute value of (cos x/2) ≡square root(1+cosx/2)

absolute value of (sin x/2) ≡square root(1-cosx/2)

Answer 1

these would come from the double angle formula of cosine

cos(2A) = cos^2 A - sin^2 A = 2cos^2 A - 1 = 1 - 2sin^2 A

then

cos(x) = 2cos^2(x/2) - 1

.. . . rearranging (or plugging it into the right side of the identity) ...

we have

|cos(x/2)| = √((1+cos x)/2)

use

cos(x) = 1 - 2sin^2(x/2)

for the next identity .. . .. .