The set s = " 1 √2 , cos x, cos 2x, cos 3x, cos 4x ( is an orthonormal set of vectors in c[−π, π] with inner product defined by (2).
(a) use trigonometric identities to write the func- tion sin4 x as a linear combination of elements of s.
(b) use part (a) and theorem 5.5.2 to find the values of the following integrals:
(a) ! π −π sin4 x cos x dx
(b) ! π −π sin4 x cos 2x dx
(c) ! π −π sin4 x cos 3x dx
(d) ! π −π sin4 x cos 4x dx