1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
  3. Ex 3.3
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Ex 3.3, 19 - Chapter 3 Class 11 Trigonometric Functions

Last updated at Dec. 13, 2024 by Teachoo

Transcript

Ex 3.3, 19 Prove that 〖sin x +〗⁡sin⁡3x /(𝑐𝑜𝑠⁡x + 𝑐𝑜𝑠⁡3x ) = tan 2x Solving L.H.S. 〖sin x +〗⁡sin⁡3x /(𝑐𝑜𝑠⁡x + 𝑐𝑜𝑠⁡3x ) We solve sin x + sin 3x & cos x + cos 3x seperately sin x + sin 3x = 2 sin ((x+3x)/2) cos ((x−3x)/2) = 2 sin (4𝑥/2) cos ((−2𝑥)/2) = 2 sin 2x cos (–x) cos x + cos 3x = 2 cos ((x+3x)/2) cos ((5x−3x)/2) = 2 cos (4𝑥/2) cos ((−2𝑥)/2) = 2 cos 2x cos (–x) Now 𝑠𝑖𝑛⁡〖𝑥 + 𝑠𝑖𝑛⁡3𝑥 〗/𝑐𝑜𝑠⁡〖𝑥 + 𝑐𝑜𝑠⁡3𝑥 〗 = (𝟐 〖 𝒔𝒊𝒏 〗⁡〖𝟐𝒙 𝒄𝒐𝒔⁡〖(−𝒙)〗 〗)/(𝟐 𝒄𝒐𝒔⁡〖 𝟐𝒙 𝒄𝒐𝒔⁡〖(−𝒙)〗 〗 ) = 𝑠𝑖𝑛⁡〖 2x〗/cos⁡〖 2x〗 = tan 2x = R.H.S Hence L.H.S = R.H.S Hence proved
  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise

    3. Ex 3.3

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Examples →
Chapter 3 Class 11 Trigonometric Functions
Serial order wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo