For π≤θ<2π given P=(1/2)cos θ−(1/4)sin 2θ−(1/8)cos 3θ+(1/(16))sin 4θ+(1/(32))cos 5θ −(1/(64))sin 6θ−(1/(128))cos 7θ+… Q=1−(1/2)sin θ−(1/4)cos 2θ+(1/8)sin 3θ+(1/(16))cos 4θ−(1/(32))sin 5θ −(1/(64))cos 6θ+(1/(128))sin 7θ+... so (P/Q)=((2(√7))/7). After sin θ=−(m/n), where m and n prime relatif. The value m+n is…


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

$For π ⩽ θ < 2 π$ $given$ $P = \frac{1}{2} \cos θ - \frac{1}{4} \sin 2 θ - \frac{1}{8} \cos 3 θ + \frac{1}{16} \sin 4 θ + \frac{1}{32} \cos 5 θ$ $- \frac{1}{64} \sin 6 θ - \frac{1}{128} \cos 7 θ + \dots$ $Q = 1 - \frac{1}{2} \sin θ - \frac{1}{4} \cos 2 θ + \frac{1}{8} \sin 3 θ + \frac{1}{16} \cos 4 θ - \frac{1}{32} \sin 5 θ$ $- \frac{1}{64} \cos 6 θ + \frac{1}{128} \sin 7 θ + . . .$ $so \frac{P}{Q} = \frac{2 \sqrt{7}}{7} . After \sin θ = - \frac{m}{n}, where m and n$ $prime relatif . The value m + n is \dots$
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