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

Ex 3.3

Ex 3.3, 1
Important

Ex 3.3, 2 Important

Ex 3.3, 3 Important

Ex 3.3, 4

Ex 3.3, 5 (i) Important

Ex 3.3, 5 (ii)

Ex 3.3, 6 Important

Ex 3.3, 7

Ex 3.3, 8 Important

Ex 3.3, 9 Important

Ex 3.3, 10

Ex 3.3, 11 Important

Ex 3.3, 12

Ex 3.3, 13 Important You are here

Ex 3.3, 14

Ex 3.3, 15

Ex 3.3, 16 Important

Ex 3.3, 17

Ex 3.3, 18 Important

Ex 3.3, 19

Ex 3.3, 20

Ex 3.3, 21 Important

Ex 3.3, 22 Important

Ex 3.3, 23 Important

Ex 3.3, 24

Ex 3.3, 25

Chapter 3 Class 11 Trigonometric Functions

Serial order wise

Last updated at June 22, 2023 by Teachoo

Ex 3.3, 13 Prove that cos2 2𝑥 – cos2 6𝑥 = sin4𝑥 sin8𝑥 Solving L.H.S. cos2 2x – cos2 6x = (cos 2x + cos 6x) (cos 2x – cos 6x) Lets calculate (cos 2x + cos 6x) and (cos 2x – cos 6x) separately cos 2x + cos 6x = 2 cos ((2x+6x)/2) cos ((2x−6x)/2) = 2 cos (8𝑥/2) cos ((−4𝑥)/2) = 2 cos 4x cos (-2x) cos 2x – cos 6x = – 2 sin ((2x+6x)/2) sin((2x−6x)/2) = – 2 sin (8𝑥/2) sin ((−4𝑥)/2) = – 2 sin 4x sin (–2x) Hence 𝒄𝒐𝒔𝟐 𝟐𝒙 – 𝒄𝒐𝒔𝟐 𝟔𝒙 = (cos2𝑥 + cos6𝑥) (cos2𝑥 – 6𝑥) = (2 cos〖4𝑥 𝒄𝒐𝒔〖(−𝟐𝒙)〗 〗 ) (−2 sin4𝑥 (𝒔𝒊𝒏〖(−𝟐𝒙)〗 )) = (2 cos〖4𝑥 𝒄𝒐𝒔〖(𝟐𝒙)〗 〗 ) (−2 sin4𝑥 (〖−𝒔𝒊𝒏〗〖(𝟐𝒙)〗 )) = (2 cos〖4𝑥 cos〖(2𝑥)〗 〗 ) (2 sin4𝑥 sin〖(2𝑥)〗 ) = (𝟐 𝒔𝒊𝒏𝟒𝒙 𝒄𝒐𝒔𝟒𝒙) (𝟐 𝒔𝒊𝒏𝟐𝒙 𝒄𝒐𝒔𝟐𝒙) We know that sin 2x = 2 sin x cos x Putting 4x instead of x And putting 2x instead of x = sin8𝑥 sin4𝑥 = R.H.S. Hence, L.H.S. = R.H.S. Hence proved