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  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise

Transcript

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 We know that 2 cos x cos y = cos (x + y) + cos (x โ€“ y) Putting x = 9๐œ‹/13 and y = ๐œ‹/13 2cos 9๐œ‹/13 cos ๐œ‹/13 = cos (9๐œ‹/13 " + " ๐œ‹/13) + cos(9๐œ‹/13 " + " ๐œ‹/13) = cos (10๐œ‹/13) + cos ((8 ๐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 (cos ๐œ‹/2 = 0)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.