Ex 3.4, 5 - Chapter 3 Class 11 Trigonometric Functions

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Ex3.4, 5 Find the general solution of the equation cos 4x = cos 2x cos 4x = cos 2x cos 4x – cos 2x = 0 – 2 sin ((4𝑥 + 2𝑥)/2) sin ((4𝑥 − 2𝑥)/2) = 0 – 2sin (6𝑥/2) sin (2𝑥/2) = 0 – 2 sin 3x sin x = 0 sin 3x sin x = 0/(−2) ⇒ 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 ⇒ sin 3x = sin 3y Given sin 3x = 0 From (1) and (2) sin 3y = 0 sin 3y = sin (0) 3y = 0 ⇒ y = 0 General solution for sin 3x = sin 3y is 3x = nπ ± (-1)n 3y where n ∈ Z Put y = 0 3x = nπ ± (-1)n 0 3x = nπ x = 𝑛𝜋/3 where n ∈ 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) ⇒ y = 0 General solution for sin x = sin y is x = nπ ± (-1)n y where n ∈ Z Put y = 0 x = nπ ± (-1)n 0 x = nπ where n ∈ Z General Solution are For sin 3x = 0, x = 𝑛𝜋/3 For sin x = 0 , x = nπ where n ∈ Z