34. [M] Let B D f1; cost; cos2 t; : : : ; cos6 tg and C D f1; cost; cos 2t; : : : ; cos 6tg. Assume the following trigonometric identities (see Exercise 37 in Section 4.1). cos 2t D 1 C 2 cos2 t cos 3t D 3 cost C 4 cos3 t cos 4t D 1 8 cos2 t C 8 cos4 t cos 5t D 5 cost 20 cos3 t C 16 cos5 t cos 6t D 1 C 18 cos2 t 48 cos4 t C 32 cos6 t Let H be the subspace of functions spanned by the functions in B. Then B is a basis for H, by Exercise 38 in Section 4.3. a. Write the B-coordinate vectors of the vectors in C, and use them to show that C is a linearly independent set in H. b. Explain why C is a