Use the half-angle identities to find the exact value of cos 15 degrees.
this is what i have so far:
cos15 degrees = cos1/2(30 degree) = sqrt (1+cos30)/2 = sqrt (1+ sqrt3/2)/ 2
but.. i don't understand how the cos30 turns into sqrt 3/2? ?

The question is: how does cos(30) =

Let's start by considering the equilateral triangle ABC in the diagram below. An equilateral triangle has equal size of angles, 60°, 60°, and 60°. Let's say the length of each side to be 2 units.

If we split this triangle into two congruent right-angled triangle, we will have the measurement of the perpendicular height to be √3 by Pythagoras theorem.

By trigonometry ratio we then have

This ratio will always work for any right angle triangle with angles 90°, 60° and 30°

Going back to the original question:

cos(15°) = cos(30°) which is cos()
let θ be 30° then cos(15°)=cos(θ/2)
by the trigonometry formula for half angle identity
cos(θ/2) = √(1+cosθ)/2
cos(15) = √(1+cos(30))/2
cos(15) = √(1+) / 2
cos(15) =