Question #13d24

1 Answer
Nov 17, 2016

see below

Explanation:

#sqrt((1+cosA)/2)=cos (A/2 )#

We will prove this by using the double argument formula for cosine.

Recall that one of the formula for #cos 2A# is #cos2A=2cos^2A-1#

So if we isolate cos A then we have

# (cos 2A+1)/2=cos^2 A#

#+-sqrt ( (1+cos2A)/2)=cos A#

So from this formula we can see that you double angle A inside the square root. Since A in this case is #1/2A# then we have #2A=2(1/2A)=A#,

#+-sqrt ( (1+cos2(1/2A))/2)=cos (1/2A)#

#:. +-sqrt((1+cosA)/2)=cos (A/2 )#