+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).
+399 We know:
\(\cos(2x)=1-2 {\sin}^{2}(x)=2{\cos}^{2}(x)-1\).
Using a clever implementation of these formulas,
\(\cos(4x)=2{\cos}^{2}(2x)-1=2{(1-2{\sin}^{2}(x))}^{2}-1\).
We get: \(\cos(4x)=8{\sin}^{4}(x)-8{\sin}^{2}(x)+1\).
