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Misc 1 - Prove 2cos pi/13 cos 9pi/13 + cos 3pi/13 + cos 5pi/13 - Miscellaneous

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Misc 1 Prove that: 2cos ๐œ‹/13 cos 9๐œ‹/13 + cos 3๐œ‹/13 + cos 5๐œ‹/13 = 0 Taking L.H.S 2cos ๐œ‹/13 cos 9๐œ‹/13 + cos 3๐œ‹/13 + cos 5๐œ‹/13 = ("cos " 10๐œ‹/13 " + cos " 8๐œ‹/13) + cos 3๐œ‹/13 + cos 5๐œ‹/13 = ("cos " 10๐œ‹/13 " + cos " 3๐œ‹/13) + ("cos " 8๐œ‹/13 " + cos " 5๐œ‹/13) = ("2 cos " ((10๐œ‹/13 + 3๐œ‹/13)/2)" . cos " ((10๐œ‹/13 โˆ’ 3๐œ‹/13)/2)) + ("2cos " ((8๐œ‹/13 + 5๐œ‹/13)/2)" . cos " ((8๐œ‹/13 โˆ’ 5๐œ‹/13)/2)) = ("2 cos " ((13๐œ‹/13)/2)" . cos " ((7๐œ‹/13)/2)) + ("2 cos " (13๐œ‹/13)/2 " . cos " (3๐œ‹/13)/2) = ("2 cos " ๐œ‹/2 " . cos " 7๐œ‹/26) + ("2 cos " ๐œ‹/2 " . cos " 3๐œ‹/26) = 2 cos ๐œ‹/2 ("cos " 7๐œ‹/26 " + cos " 3๐œ‹/26) = 2 ร— 0 ("cos " 7๐œ‹/26 " + cos " 3๐œ‹/26) = 0 = R.H.S. Hence L.H.S. =R.H.S. Hence proved

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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