Question

Question #13d24

Answer 1

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 )`