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Example 23 - Chapter 3 Class 11 Trigonometric Functions (Term 2)
Last updated at March 6, 2018 by Teachoo
Examples
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Example 2 Important
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Example 5 Important
Example 6 Important
Example 7 Important
Example 8
Example 9 Important
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Example 11 Important
Example 12
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Example 14
Example 15
Example 16 Important
Example 17 Important
Example 18
Example 19
Example 20 Deleted for CBSE Board 2023 Exams
Example 21 Deleted for CBSE Board 2023 Exams
Example 22 Important Deleted for CBSE Board 2023 Exams
Example 23 Deleted for CBSE Board 2023 Exams You are here
Example 24 Important Deleted for CBSE Board 2023 Exams
Example 25 Important
Example 26
Example 27 Important
Example 28 Important
Example 29 Important
Chapter 3 Class 11 Trigonometric Functions
Serial order wise
- Ex 3.1
- Ex 3.2
- Ex 3.3
- Ex 3.4
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Examples
- Miscellaneous
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
