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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 – cos 2x = 0 cos 3x + cos x – cos 2x = 0 (cos 3x + cos x) – cos 2x = 0 2 cos ((3π‘₯ + π‘₯)/2) . cos ((3π‘₯ βˆ’ π‘₯)/2) – cos 2x = 0 2 cos (4π‘₯/2) . cos (2π‘₯/2) – cos 2x = 0 2 cos (2x) . cos x – cos 2x = 0 cos (2x) (2cos x – 1) = 0 Hence cos 2x = 0 or (2cos x – 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 β‡’ cos 2x = cos 2y Given cos 2x = 0 From (1) and (2) cos 2y = 0 cos 2y = cos 90Β° cos 2y = cos πœ‹/2 2y = πœ‹/2 General solution for cos 2x = cos 2y is given by 2x = 2nΟ€ Β± 2y where n ∈ Z putting 2y = πœ‹/2 2x = 2nΟ€ Β± πœ‹/2 x = 1/2 (2nΟ€ Β± πœ‹/2) x = nΟ€ Β± πœ‹/2 General solution for cos x = 𝟏/𝟐 Let cos x = cos y Given cos x = 1/2 From (3) and (4) cos y = 1/2 cos (y) = cos (πœ‹/3) β‡’ y = πœ‹/3 General solution for cos x = cos y is x = 2nΟ€ Β± y where n ∈ Z putting y = πœ‹/3 x = nΟ€ Β± πœ‹/3 where n ∈ Z Hence General Solution is For cos 2x = 0, x = nΟ€ Β± πœ‹/2 & for cos x = 1/2 , x = nΟ€ Β± πœ‹/3 where n ∈ 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.