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 )