Question: We note that a function can be written as a polynomial in sin x (or cos x) if it is of the form p(sin x) (or p(cos x)) for some polynomial p(x). For example, cos 2x can be written as a polynomial in sin x because cos(2x)=1 - 2 sin2 x = p(sin x), where p(x)=1 - 2x2.
Use the trigonometric capabilities of your computer algebra system to express cos(4x) as a polynomial in
(a) sin x
(b) cos x.