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 /13 cos 9 /13 + cos 3 /13 + cos 5 /13 = 0 Taking L.H.S 2cos /13 cos 9 /13 + cos 3 /13 + cos 5 /13 = ("cos " 10 /13 " + cos " 8 /13) + cos 3 /13 + cos 5 /13 = ("cos " 10 /13 " + cos " 3 /13) + ("cos " 8 /13 " + cos " 5 /13) = ("2 cos " ((10 /13 + 3 /13)/2)" . cos " ((10 /13 3 /13)/2)) + ("2cos " ((8 /13 + 5 /13)/2)" . cos " ((8 /13 5 /13)/2)) = ("2 cos " ((13 /13)/2)" . cos " ((7 /13)/2)) + ("2 cos " (13 /13)/2 " . cos " (3 /13)/2) = ("2 cos " /2 " . cos " 7 /26) + ("2 cos " /2 " . cos " 3 /26) = 2 cos /2 ("cos " 7 /26 " + cos " 3 /26) = 2 0 ("cos " 7 /26 " + cos " 3 /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 has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.