Subscribe to our Youtube Channel - https://you.tube/teachoo
Example 16 - Chapter 3 Class 11 Trigonometric Functions
Last updated at Feb. 13, 2020 by Teachoo
Transcript
Example 16 Prove that ๐๐๐ โกใ7๐ฅ + ๐๐๐ โก5๐ฅ ใ/๐ ๐๐โกใ7๐ฅ โ ๐ ๐๐โก5๐ฅ ใ = cot x Taking L.H.S. We solve cos 7x + cos 5x & sin 7x โ sin 5x separately cos x + cos y = 2 cos (๐ฅ + ๐ฆ)/2 cos (๐ฅ โ ๐ฆ)/2 Putting x = 7x & y = 5x cos 7x + cos 5x = 2 cos ((7๐ฅ + 5๐ฅ)/2) cos ((7๐ฅ โ 5๐ฅ)/2) = 2 cos (12๐ฅ/2) cos (2๐ฅ/2) = 2 cos 6x cos x sin x โ sin y = 2 cos (๐ฅ + ๐ฆ)/2 sin (๐ฅ โ ๐ฆ)/2 Putting x = 7x & y = 5x sin 7x โ sin 5x = 2 cos ((7๐ฅ + 5๐ฅ)/2) sin((7๐ฅ โ 5๐ฅ)/2) = 2 cos (12๐ฅ/2) sin (2๐ฅ/2) = 2 cos 6x sin x Now ใ๐๐๐ ใโกใ7๐ฅ + ๐๐๐ โก5๐ฅ ใ/๐ ๐๐โกใ7๐ฅ โ ๐ ๐๐โก5๐ฅ ใ = (2 ใ ๐๐๐ ใโกใ6x ๐๐๐ โก๐ฅ ใ)/(2 ๐๐๐ โกใ 6๐ฅ si๐โก๐ฅ ใ ) = ๐๐๐ โกใ ๐ฅใ/๐ ๐๐โกใ ๐ฅใ = cot x = R.H.S. Hence L.H.S. = R.H.S. Hence proved
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 You are here
Example 17 Important
Example 18
Example 19 Important
Example 20 Not in Syllabus - CBSE Exams 2021
Example 21 Not in Syllabus - CBSE Exams 2021
Example 22 Important Not in Syllabus - CBSE Exams 2021
Example 23 Not in Syllabus - CBSE Exams 2021
Example 24 Important Not in Syllabus - CBSE Exams 2021
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.