Find the general solution of the following equation: sin x + sin 3 x + sin 5 x = 0

Given: sin x + sin 3 x + sin 5 x = 0 sin 3 x + 2 sin 3 x cos 2 x = 0 We know sin C + sin D = 2 sin ( C + D ) 2 × cos ( C - D ) 2 sin 3 x ( 1 + 2 cos 2 x ) = 0 sin 3 x = 0 or cos 2 x = - 1 2 = cos 2 π 3 Formula used: sin θ = 0 ⇒ θ = n π , n ∈ I and cos θ = cos α ⇒ θ = 2 k π ± α , k ∈ I 3 x = n π or 2 x = 2 k π ± 2 π 3 x = n π 3 or x = k π ± π 3 where n , k ∈ I So general solution is x = n π 3 or x = k π ± π 3 where n , k ∈ I

Find the general solution of the following equation: 3 cos x + sin x = 1

Given: 3 cos x + sin x = 1 Divide 2 on both sides 3 cos x + sin x 2 = 1 2 Apply cos ( x - y ) = cos x cos y + sin x sin y cos x - π 6 = 1 2 = cos π 3 Formula used: cos θ = cos α ⇒ θ = 2 n π ± α , where n ∈ I By using above formula, we have x - π 6 = 2 n π ± π 3 ⇒ x = 2 n π ± π 3 + π 6 x = 2 n π + π 3 + π 6 or x = 2 n π - π 3 + π 6 x = 2 n π + π 2 or x = 2 n π - π 6 where n ∈ I So general solution is x = 2 n π + π 2 or x = 2 n π - π 6 where n ∈ I .

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Senior Secondary School Mathematics FOR CLASS 11>Trigonometry>Chapter 17 - Trigonometric Equations>EXERCISE

R S Aggarwal Solutions for Exercise 1: EXERCISE

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Exercise 1: EXERCISE

Attempt the practice questions from Exercise 1: EXERCISE with hints and solutions to strengthen your understanding. Senior Secondary School Mathematics FOR CLASS 11 solutions are prepared by Experienced Embibe Experts.