Using Prob. 3, derive the orthogonality of 1, cos x, sin x, cos 2x, sin 2x,

Using Prob. 3, derive the orthogonality of 1, cos πx, sin πx, cos 2πx, sin 2πx, · · · on -1 ≤ x ≤ 1 (r(x) = 1) from that of 1, cos x, sin x, cos 2x, sin 2x, · · · on -π ≤ x ≤ π.

Data from Prob. 3

Show that if the functions y₀(x), y₁(x), · · · form an orthogonal set on an interval α ≤ x ≤ b (with r(x) = 1), then the functions y₀(ct + k), y₁(ct + k), · · ·, c > 0, form an orthogonal set on the interval (α - k)/c ≤ t ≤ (b - k)/c.