38   Question 14 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 39   Question 14 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 14 is 10 marks) 40   15. In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Given that the first three terms of a geometric series are 12 cos θ            5 + 2 sin θ            and            6 tan θ (a) show that 4 sin 2 θ − 52 sin θ + 25 = 0 (3) Given that θ is an obtuse angle measured in radians, (b) solve the equation in part (a) to find the exact value of θ (2) (c) show that the sum to infinity of the series can be expressed in the form k (1 −  3 ) where k is a constant to be found. 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