(a) Recall that 2 sin u cos v = sin(u+v)+sin(u-v) and 2 cos u sin v...

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(a) Recall that 2 sin u cos v = sin(u+v)+sin(u-v) and 2 cos u sin v = sin(u + v)- sin(u - v). Prove that 1/2+ cos r + cos(2r) ++ cos(nr)D (b) If F(x) = G(t) for any two values r and t, then prove that F(r) = A and G(t) = for a constant A. sin(n + 1/2)z 2 sin(r/2) %3D %3D (a) Recall that 2 sin u cos v = sin(u+v)+sin(u-v) and 2 cos u sin v = sin(u + v)- sin(u - v). Prove that 1/2+ cos r + cos(2r) ++ cos(nr)D (b) If F(x) = G(t) for any two values r and t, then prove that F(r) = A and G(t) = for a constant A. sin(n + 1/2)z 2 sin(r/2) %3D %3D