1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
  3. Ex 3.3
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Ex 3.3, 20 - Chapter 3 Class 11 Trigonometric Functions

Last updated at Dec. 13, 2024 by Teachoo

Transcript

Ex 3.3, 20 Prove that 〖sin x − 〗⁡sin⁡3x /(sin2⁡x − cos2⁡x ) = 2 sin x Solving L.H.S. 〖sin x −〗⁡sin⁡3x /(sin2⁡x − cos2⁡x ) We solve sin x – sin 3x & sin2 x – cos2 x separately sin x – sin 3x = 2 cos ((x + 3x)/2) sin((x − 3x)/2) = 2 cos (4𝑥/2) sin ((−2𝑥)/2) = 2 cos 2x sin (–x) sin2 x – cos2 x = – cos 2x We know that cos 2x = cos2 x – sin2 x cos 2x = – ( sin2 x – cos2 x) Thus, −( sin2 x – cos2 x) = cos 2x − ( sin2 x – cos2 x) = – cos 2x Now, sin⁡〖𝑥 − sin⁡3𝑥 〗/sin2⁡〖𝑥 − cos2⁡𝑥 〗 = 〖𝟐 𝒄𝒐𝒔 〗⁡〖𝟐𝒙 〖 𝒔𝒊𝒏〗⁡〖(−𝒙)〗 〗/〖−𝒄𝒐𝒔〗⁡𝟐𝒙 = 〖2 𝑐𝑜𝑠〗⁡〖2𝑥 〖(− sin〗⁡𝑥)〗/〖−𝑐𝑜𝑠〗⁡2𝑥 = 2sin x = 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

    Examples →
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