How do you find the exact values of cos 15 using the half angle formula?

1 Answer
Aug 30, 2015

color(red)(cos15 = sqrt(2 +sqrt3)/2)cos15=2+32

Explanation:

The cosine half-angle formula is

cos(x/2) = ±sqrt((1 + cos x) / 2)cos(x2)=±1+cosx2

The sign is positive if x/2x2 is in the first or fourth quadrant and negative if x/2x2 is in the second or third quadrant.

15° is in the first quadrant, so the sign is positive.

15= 30/2

cos15 = cos(30/2) = sqrt((1+cos30)/2)

cos15 = sqrt((1 + sqrt3/2)/2) = sqrt((2 + sqrt3)/4)

cos15 = sqrt(2 +sqrt3)/2