Calculate the difference cos75-cos15.

Since the functions are matching, we'll use the
identity:

cos a - cos b = 2 sin [(a+b)/2]*sin
[(b-a)/2]

a = 75 and b =
15

cos 75 - cos 15 = 2 sin
[(75+15)/2]*sin[(15-75)/2]

cos 75 - cos 15 = 2 sin
45*sin(-30)

Since the sine function is odd, then sin(-30) =
-sin 30

cos 75 - cos 15 = -2
(sqrt2/2)*(1/2)

cos 75 - cos 15 = -
(sqrt2/2)

The requested difference is: cos 75
- cos 15 = - (sqrt2/2).