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

Transcript

Ex 3.4, 6 Find the general solution of the equation cos 3x + cos x โ€“ cos 2x = 0 cos 3x + cos x โ€“ cos 2x = 0 (cos 3x + cos x) โ€“ cos 2x = 0 2 cos ((3๐‘ฅ + ๐‘ฅ)/2) . cos ((3๐‘ฅ โˆ’ ๐‘ฅ)/2) โ€“cos 2x = 0 2 cos (4๐‘ฅ/2) . cos (2๐‘ฅ/2) โˆ’cos 2x = 0 2 cos 2x . cos x โ€“ cos 2x = 0 cos 2x (2cos x โ€“ 1) = 0 We know that cos x + cos y = 2 cos ((๐‘ฅ + ๐‘ฆ)/2) cos ((๐‘ฅ โˆ’ ๐‘ฆ)/2) Replacing x by 3x & y by x Hence We find general solutions of both separately General solution for cos 2x = 0 Given cos 2x = 0 Thus, general solution is 2x = (2n + 1) ๐œ‹/2 x = (2n + 1) ๐…/๐Ÿ’ where n โˆˆ Z (2cos x โ€“ 1) = 0 2cos x = 1 cos x = 1/2 General solution for cos x = ๐Ÿ/๐Ÿ Let cos x = cos y Given cos x = 1/2 From (3) and (4) cos y = 1/2 cos y = cos (๐œ‹/3) y = ๐œ‹/3 Rough We know that cos 60ยฐ = 1/2 So, 60ยฐ = 60 ร— ๐œ‹/180 = ๐œ‹/3 General solution for cos x = cos y is x = 2nฯ€ ยฑ y where n โˆˆ Z Putting y = ๐œ‹/3 x = 2nฯ€ ยฑ ๐œ‹/3 where n โˆˆ Z Hence General Solution is For cos 2x = 0, x = (2n + 1) ๐…/๐Ÿ’ Or For cos x = 1/2 , x = 2nฯ€ ยฑ ๐…/๐Ÿ‘ where n โˆˆ Z

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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.