Using the addition formulas we've learned, we can develop new identities for sin and cos that can be used to express the sine and cosine of half-angles in terms of the cosine of a whole angle. Recall the addition formula:
(1) - cos (a + b) = (cos a)(cos b) – (sin a)(sin b)
Simplify.
Using the identity (sin a)2 + (cos a)2 = 1, replace in (2):