Home  18.013A  Chapter 2  Section 2.3 


Find expressions for (sin t/2)^{2} and (cos t/2)^{2} from the Pythagorean theorem and the cosine addition theorem.
Solution:
The Pythagorian theorem is the statement (sin x)^{2} + (cos x)^{2 }= 1 (or we can interpret it to be that statement).
If we apply this equation for and also use the cosine addition theorem
cos (u + v) = (cos u)(cos v)  (sin u)(sin v)
for , we get
and we can add and subtract these equations from one another to get
