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  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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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) โ€“ cos 2x = 0 2 cos (2x) . cos x โ€“ cos 2x = 0 cos (2x) (2cos x โ€“ 1) = 0 Hence cos 2x = 0 or (2cos x โ€“ 1) = 0 cos 2x = 0 or 2cos x = 1 cos 2x = 0 or cos x = 1/2 We find general solutions of both separately General solution for cos 2x = 0 Let cos x = cos y โ‡’ cos 2x = cos 2y Given cos 2x = 0 From (1) and (2) cos 2y = 0 cos 2y = cos 90ยฐ cos 2y = cos ๐œ‹/2 2y = ๐œ‹/2 General solution for cos 2x = cos 2y is given by 2x = 2nฯ€ ยฑ 2y where n โˆˆ Z putting 2y = ๐œ‹/2 2x = 2nฯ€ ยฑ ๐œ‹/2 x = 1/2 (2nฯ€ ยฑ ๐œ‹/2) x = nฯ€ ยฑ ๐œ‹/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) โ‡’ y = 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 = nฯ€ ยฑ ๐œ‹/3 where n โˆˆ Z Hence General Solution is For cos 2x = 0, x = nฯ€ ยฑ ๐œ‹/2 & for cos x = 1/2 , x = nฯ€ ยฑ ๐œ‹/3 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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.