1. Chapter 3 Class 11 Trigonometric Functions
2. Serial order wise
3. Ex 3.4

Transcript

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 โ 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/(โ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 โ Z Put y = 0 3x = nฯ ยฑ (-1)n 0 3x = nฯ x = ๐๐/3 where n โ 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 โ Z Put y = 0 x = nฯ ยฑ (-1)n 0 x = nฯ where n โ Z General Solution are For sin 3x = 0, x = ๐๐/3 For sin x = 0 , x = nฯ where n โ Z

Ex 3.4