If , match Column I with Column II. | Column I | Column II | |---|---| | (a) | (p) |…

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

If fn(θ)=sin⁡θ+sin⁡3θ+sin⁡5θ+⋯+sin⁡((2n−1)θ)cos⁡θ+cos⁡3θ+cos⁡5θ+⋯+cos⁡((2n−1)θ)f_n(\theta)=\frac{\sin\theta+\sin3\theta+\sin5\theta+\dots+\sin((2n-1)\theta)}{\cos\theta+\cos3\theta+\cos5\theta+\dots+\cos((2n-1)\theta)}, match Column I with Column II.
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) 11
(1) (a) →\to (p); (b) →\to (q); (c) →\to (r); (d) →\to (s), (t) (2) (a) →\to (t); (b) →\to (p); (c) →\to (r); (d) →\to (q) (3) (a) →\to (q); (b) →\to (r); (c) →\to (s); (d) →\to (t) (4) (a) →\to (r), (t); (b) →\to (s); (c) →\to (p); (d) →\to (q)

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