For-pi-lt-2pi-given-P-1-2-cos-1-4-sin-2-1-8-cos-3-1-16-sin-4-1-32-cos-5-1-64-sin-6-1-128-cos-7-Q-1-1-2-sin-1-4-cos-2-1-8-sin-3-1-16-cos-4-1-32-sin-5-1-

Question Number 43792 by gunawan last updated on 15/Sep/18

For π ⩽ θ < 2 π

given

P = \frac{1}{2} \cos θ - \frac{1}{4} \sin 2 θ - \frac{1}{8} \cos 3 θ + \frac{1}{16} \sin 4 θ + \frac{1}{32} \cos 5 θ

- \frac{1}{64} \sin 6 θ - \frac{1}{128} \cos 7 θ + \dots

Q = 1 - \frac{1}{2} \sin θ - \frac{1}{4} \cos 2 θ + \frac{1}{8} \sin 3 θ + \frac{1}{16} \cos 4 θ - \frac{1}{32} \sin 5 θ

- \frac{1}{64} \cos 6 θ + \frac{1}{128} \sin 7 θ + \dots

so \frac{P}{Q} = \frac{2 \sqrt{7}}{7} . After \sin θ = - \frac{m}{n}, where m and n

prime relatif . The value m + n is \dots