Example 16 - Chapter 3 Class 11 Trigonometric Functions

Last updated at May 29, 2023 by Teachoo

Example 16 - Prove cos 7x + cos 5x / sin 7x - sin 5x = cot x

Example 16 - Chapter 3 Class 11 Trigonometric Functions - Part 2

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Book a free demo

Transcript

Example 16 Prove that 𝑐𝑜𝑠⁡〖7𝑥 + 𝑐𝑜𝑠⁡5𝑥 〗/𝑠𝑖𝑛⁡〖7𝑥 − 𝑠𝑖𝑛⁡5𝑥 〗 = cot x Taking L.H.S. We solve cos 7x + cos 5x & sin 7x – sin 5x separately cos x + cos y = 2 cos (𝑥 + 𝑦)/2 cos (𝑥 − 𝑦)/2 Putting x = 7x & y = 5x cos 7x + cos 5x = 2 cos ((7𝑥 + 5𝑥)/2) cos ((7𝑥 − 5𝑥)/2) = 2 cos (12𝑥/2) cos (2𝑥/2) = 2 cos 6x cos x sin x – sin y = 2 cos (𝑥 + 𝑦)/2 sin (𝑥 − 𝑦)/2 Putting x = 7x & y = 5x sin 7x – sin 5x = 2 cos ((7𝑥 + 5𝑥)/2) sin((7𝑥 − 5𝑥)/2) = 2 cos (12𝑥/2) sin (2𝑥/2) = 2 cos 6x sin x Now 〖𝑐𝑜𝑠 〗⁡〖7𝑥 + 𝑐𝑜𝑠⁡5𝑥 〗/𝑠𝑖𝑛⁡〖7𝑥 − 𝑠𝑖𝑛⁡5𝑥 〗 = (2 〖 𝑐𝑜𝑠 〗⁡〖6x 𝑐𝑜𝑠⁡𝑥 〗)/(2 𝑐𝑜𝑠⁡〖 6𝑥 si𝑛⁡𝑥 〗 ) = 𝑐𝑜𝑠⁡〖 𝑥〗/𝑠𝑖𝑛⁡〖 𝑥〗 = cot x = R.H.S. Hence L.H.S. = R.H.S. Hence proved

Next: Example 17 Important → Ask a doubt

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular