Subscribe to our Youtube Channel - https://you.tube/teachoo

Last updated at March 6, 2018 by Teachoo

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

Examples

Example 1

Example 2

Example 3

Example 4

Example 5 Important

Example 6 Important

Example 7 Important

Example 8

Example 9 Important

Example 10

Example 11 Important

Example 12

Example 13

Example 14

Example 15

Example 16 Important

Example 17 Important

Example 18

Example 19 Important

Example 20

Example 21

Example 22 Important

Example 23 You are here

Example 24 Important

Example 25 Important

Example 26 Important

Example 27 Important

Example 28 Important

Example 29 Important

Chapter 3 Class 11 Trigonometric Functions

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.