Problem: Let x=cos36ββcos72β. Then x equals
Answer Choices:
A. 1/3
B. 1/2
C. 3β6β
D. 23ββ3
E. none of these
Solution:
Let w=cos36β and let y=cos72β. Applying the identities
cos2ΞΈ=2cos2ΞΈβ1 and cos2ΞΈ=1β2sin2ΞΈ
with ΞΈ=36β in the first identity and ΞΈ=18β in the second identity, yields
y=2w2β1 and w=1β2y2
Adding these last two equations and dividing the result by w+y yields the desired result.