+68 Find constants a, b, c, d and e such that cos4x=a(sin^4)x+b(sin^3)x+c(sin^2)x+d(sin)x+e for all angles x. In other words, write cos(4x) as a polynomial in sin(x).
+410 We know:
cos(2x)=1−2sin2(x)=2cos2(x)−1.
Using a clever implementation of these formulas,
cos(4x)=2cos2(2x)−1=2(1−2sin2(x))2−1.
We get: cos(4x)=8sin4(x)−8sin2(x)+1.
