Question: 3. [Maximum mark: 8] The first three terms of a geometric sequence are sin x, sin 2x, and 4 sin x cos x, -; S

3. [Maximum mark: 8] The first three terms of a geometric sequence are sin x, sin 2x, and 4 sin x cos x, -; S x S (a) Show that the common ratio r is 2 cos x. [1] (b) Find the set of values of x for which the geometric series sin x + sin 2x + 4 sinxcos x + ... converges. [4] Consider x = arccos- , x > 0 (c) Show that the sum to infinity of this series is Vis [3] 2

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