Verified answer

The half-angle formula states that cos (x/2) = +,- sqrt[(1+cos x)/2].

Since the angle of 15° is exactly half of 30° and the cos 30° is a common angle known to be sqrt(3)/2, you can use this fact along with the half-angle formula to get your answer.

cos 15° = sqrt[(1+sqrt(3)/2)/2]

cos 15° = sqrt[(1/2 + sqrt(3)/4]

cos 15° = [1+sqrt(3)]/[2*sqrt(2)]

cos15°=√[(1+cos30°)/2]

=√[{1+(√3)/2}/2]

=√[1/2+(√3)/4]

cos(a-b) =cos(a)cos(b) +sin(a)sin(b)

cos(45)=sin(45) =sqrt(2)/2

cos(30)=sqrt(3)/2

sin(30) = 1/2

cos(45-30) = sqrt(6)/4 + 1/4

cos (45-30) = ( sqrt (6) - 1 ) / 4

hope it helps