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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?

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?

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Grade:12th pass

1 Answers

Aditya Gupta
2081 Points
4 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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