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Grade 12th passTrigonometry

This problem is from the trigonometry chapter ` Transformations of sums and products` . I am stuck with this problem. Can anyone pls suggest me how to solve this?

Question image for This problem is from the trigonometry chapter ` Tr
Profile image of Ela
8 Years agoGrade 12th pass
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1 Answer

Profile image of Aditya Gupta
8 Years ago
the sum can be written as S=∑1/(cosa+cos(2r+1)a), r being from 1 to n
now , S= ∑1/2cos(r+1)acos(ra)
now, 2S*sina= ∑(sin((r+1)a – ra)/cos(r+1)acos(ra))
=  ∑tan(r+1)a – tanra [using sin(a-b)= sinacosb – sinbcosa]
the above sum telescopes, giving
2S*sina= tan(n+1)a-tana
or S= coseca(tan(n+1)a-tana)/2

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