If fn(θ)=sin⁡θ+sin⁡3θ+sin⁡5θ+⋯+sin⁡((2n−1)θ)sin⁡θ+cos⁡θ+cos⁡5θ+⋯+cos⁡((2n−1)θ)f_n(\theta) = \frac{\sin \theta + \sin 3\theta + \sin 5\theta + \dots + \sin((2n-1)\theta)}{\sin \theta + \cos \theta + \cos 5\theta + \dots + \cos((2n-1)\theta)}…

Problem

If fn(θ)=sin⁡θ+sin⁡3θ+sin⁡5θ+⋯+sin⁡((2n−1)θ)sin⁡θ+cos⁡θ+cos⁡5θ+⋯+cos⁡((2n−1)θ)f_n(\theta) = \frac{\sin \theta + \sin 3\theta + \sin 5\theta + \dots + \sin((2n-1)\theta)}{\sin \theta + \cos \theta + \cos 5\theta + \dots + \cos((2n-1)\theta)}
Column IColumn II
(A) f3(π12)f_3\left(\frac{\pi}{12}\right)(p) 2−1\sqrt{2} - 1
(B) f4(π32)f_4\left(\frac{\pi}{32}\right)(q) 2−32 - \sqrt{3}
(C) f6(π16)f_6\left(\frac{\pi}{16}\right)(r) 2+1\sqrt{2} + 1
(D) f7(π84)f_7\left(\frac{\pi}{84}\right)(s) 2+32 + \sqrt{3}
(t) 1
a. A →\to (p); B →\to (q); C →\to (r); D →\to (s, t) b. A →\to (t); B →\to (p); C →\to (r); D →\to (q) c. A →\to (q); B →\to (r); C →\to (s); D →\to (t) d. A →\to (r, t); B →\to (s); C →\to (p); D →\to (q)

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