Problem: Let x=cos36∘−cos72∘. Then x equals
Answer Choices:
A. 1/3
B. 1/2
C. 3−6
D. 23−3
E. none of these
Solution:
Let w=cos36∘ and let y=cos72∘. Applying the identities
cos2θ=2cos2θ−1 and cos2θ=1−2sin2θ
with θ=36∘ in the first identity and θ=18∘ in the second identity, yields
y=2w2−1 and w=1−2y2
Adding these last two equations and dividing the result by w+y yields the desired result.