Check sibling questions

Example 23 - Solve sin 2x - sin 4x + sin 6x = 0 - Chapter 3

Example 23 - Chapter 3 Class 11 Trigonometric Functions - Part 2
Example 23 - Chapter 3 Class 11 Trigonometric Functions - Part 3
Example 23 - Chapter 3 Class 11 Trigonometric Functions - Part 4

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Example 23 Solve sin 2x sin 4x + sin 6x = 0. sin 2x sin 4x + sin 6x = 0 (sin 6x + sin 2x) sin 4x = 0 2 sin ((6 + 2 )/2) cos ((6 2 )/2) sin 4x = 0 2 sin (8 /2) cos (4 /2) sin 4x = 0 2 sin 4x cos (2x) sin 4x = 0 sin 4x (2 cos (2x) 1) = 0 Hence sin 4x = 0 or 2cos 2x 1 = 0 sin 4x = 0 or 2cos 2x = 1 sin 4x = 0 or cos 2x = 1/2 We need to find general solution both separately General solution for sin 4x = 0 Let sin x = sin y sin 4x = sin 4y Given sin 4x = 0 From (1) and (2) sin 4y = 0 sin 4y = sin (0) 4y = 0 y = 0 General solution for sin 4x = sin 4y is 4x = n (-1)n 4y where n Z Put y = 0 4x = n (-1)n 0 4x = n x = /4 where n Z General solution for cos 2x = / Let cos x = cos y cos 2x = cos 2y Given cos 2x = 1/2 From (3) and (4) cos 2y = 1/2 cos (2y) = cos ( /3) 2y = /3 General solution for cos 2x = cos 2y is 2x = 2n 2y where n Z putting 2y = /3 2x = n /3 x = 1/2 (2n /3) x =2 /2 1/2 /3 x = n /6 where n Z Hence General Solution is For sin4x = 0, x = /4 and for cos 2x = 1/2 , x = n /6 where n Z

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.