MENU

Chapter 3 Trigonometric Functions Ex 3.3 Solutions

Question - 11 : - Prove that: 

Answer - 11 : - Consider

Using the formula

Question - 12 : - Prove that: sin2 6x – sin2 4x =sin 2x sin 10x

Answer - 12 : -


Question - 13 : - Prove that: cos2 2x – cos2 6x =sin 4x sin 8x

Answer - 13 : -


We get
= [2 cos 4x cos (-2x)] [-2 sin 4x sin (-2x)]
It can be written as
= [2 cos 4x cos 2x] [–2 sin 4x (–sin 2x)]
So we get
= (2 sin 4x cos 4x) (2 sin 2x cos 2x)
= sin 8x sin 4x
= RHS

Question - 14 : - Prove that: sin 2x + 2sin 4x + sin 6x = 4cos2 x sin4x

Answer - 14 : -


By furthersimplification

= 2 sin 4x cos (–2x) + 2 sin 4x

It can be written as

= 2 sin 4x cos2x + 2 sin 4x

Taking common terms

= 2 sin 4x (cos2x + 1)

Using the formula

= 2 sin 4x (2 cos2 x –1 + 1)

We get

= 2 sin 4x (2 cos2 x)

= 4cos2 x sin4x

= R.H.S.

Question - 15 : - Prove that: cot 4x (sin 5x + sin 3x) = cot x (sin5x – sin 3x)

Answer - 15 : -

Consider
LHS = cot 4x (sin 5x + sin 3x)
It can be written as
 
Using the formula
= 2 cos 4x cos x
Hence, LHS = RHS.

Question - 16 : - Prove that:  

Answer - 16 : -

Consider
 
Using the formula

Question - 17 : - Prove that: 

Answer - 17 : -


Question - 18 : - Prove that: 

Answer - 18 : -


Question - 19 : - Prove that: 

Answer - 19 : -


Question - 20 : - Prove that: 

Answer - 20 : -


Free - Previous Years Question Papers
Any questions? Ask us!
NodeJS Interview Questions Answers
ASP.Net Interview Questions Answers
Interview Questions Answers
×