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Ex 3.4, 5 - Find general solution of cos 4x = cos 2x - Chapter 3 - Finding general solutions

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Ex3.4, 5 Find the general solution of the equation cos 4x = cos 2x cos 4x = cos 2x cos 4x โ€“ cos 2x = 0 โ€“ 2 sin ((4๐‘ฅ + 2๐‘ฅ)/2) sin ((4๐‘ฅ โˆ’ 2๐‘ฅ)/2) = 0 โ€“ 2sin (6๐‘ฅ/2) sin (2๐‘ฅ/2) = 0 โ€“ 2 sin 3x sin x = 0 sin 3x sin x = 0/(โˆ’2) โ‡’ sin 3x sin x = 0 So, either sin 3x = 0 or sin x = 0 We solve sin 3x = 0 & sin x = 0 separately General solution for sin 3x = 0 Let sin x = sin y โ‡’ sin 3x = sin 3y Given sin 3x = 0 From (1) and (2) sin 3y = 0 sin 3y = sin (0) 3y = 0 โ‡’ y = 0 General solution for sin 3x = sin 3y is 3x = nฯ€ ยฑ (-1)n 3y where n โˆˆ Z Put y = 0 3x = nฯ€ ยฑ (-1)n 0 3x = nฯ€ x = ๐‘›๐œ‹/3 where n โˆˆ Z General solution for sin x = 0 Let sin x = sin y Given sin x = 0 From (1) and (2) sin y = 0 sin y = sin (0) โ‡’ y = 0 General solution for sin x = sin y is x = nฯ€ ยฑ (-1)n y where n โˆˆ Z Put y = 0 x = nฯ€ ยฑ (-1)n 0 x = nฯ€ where n โˆˆ Z General Solution are For sin 3x = 0, x = ๐‘›๐œ‹/3 For sin x = 0 , x = nฯ€ where n โˆˆ Z

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