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Ex 3.4, 6 - Find general solution of cos 3x + cos x - cos 2x = 0

Ex 3.4, 6 - Chapter 3 Class 11 Trigonometric Functions - Part 2
Ex 3.4, 6 - Chapter 3 Class 11 Trigonometric Functions - Part 3 Ex 3.4, 6 - Chapter 3 Class 11 Trigonometric Functions - Part 4

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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) βˆ’cos 2x = 0 2 cos 2x . cos x – cos 2x = 0 cos 2x (2cos x – 1) = 0 We know that cos x + cos y = 2 cos ((π‘₯ + 𝑦)/2) cos ((π‘₯ βˆ’ 𝑦)/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) πœ‹/2 x = (2n + 1) 𝝅/πŸ’ where n ∈ Z (2cos x – 1) = 0 2cos x = 1 cos x = 1/2 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) y = πœ‹/3 Rough We know that cos 60Β° = 1/2 So, 60Β° = 60 Γ— πœ‹/180 = πœ‹/3 General solution for cos x = cos y is x = 2nΟ€ Β± y where n ∈ Z Putting y = πœ‹/3 x = 2nΟ€ Β± πœ‹/3 where n ∈ Z Hence General Solution is For cos 2x = 0, x = (2n + 1) 𝝅/πŸ’ Or For cos x = 1/2 , x = 2nΟ€ Β± 𝝅/πŸ‘ where n ∈ Z

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.