Ex 3.3, 12 - Chapter 3 Class 11 Trigonometric Functions

Last updated at Dec. 13, 2024 by

Ex 3.3, 12 - Prove that sin2 6x - sin2 4x = sin⁡2x sin⁡10x - Ex 3.3

part 2 - Ex 3.3, 12 - Ex 3.3 - Serial order wise - Chapter 3 Class 11 Trigonometric Functions

Remove Ads

Transcript

Ex 3.3, 12 Prove that sin2 6𝑥 – sin2 4𝑥 = sin⁡2𝑥 sin⁡10𝑥 Solving L.H.S. sin2 6x – sin2 4x = (sin 6x + sin 4x) (sin 6x – sin 4x) Lets calculate (sin 6x + sin 4x) and (sin 6x – sin 4x) separately sin 6x + sin 4x = 2 sin ((6x+4x)/2) cos ((6x−4x)/2) = 2sin (10𝑥/2) cos (2𝑥/2) = 2sin 5x cos x sin 6x – sin 4x = 2 cos ((6x+4x)/2) sin((6x−4x)/2) = 2 cos (10𝑥/2) sin (2𝑥/2) = 2 cos 5x sin x Hence sin2 6x – sin2 4x = (sin 6x + sin 4x) (sin 6x – sin 4x) = (2 sin 5x cos x) (2 cos 5x sin x) = (2 sin 5x cos 5x) . (2 sin x cos x) = (sin 10x) × (sin 2x) = R.H.S. Hence, L.H.S. = R.H.S. Hence proved

Davneet Singh's photo - Co-founder, Teachoo

Made by

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