Question 1.
Express the following as a sum or difference of two trigonometric functions.
i. 2sin 4x cos 2x
iii. 2cos 4θ cos 2θ
iv. 2cos 35° cos 75°
Solution:
i. 2sin 4x cos 2x = sin(4x + 2x ) + sin (4x – 2x)
= sin 6x + sin 2x
ii.
![Maharashtra Board Class 11 Maths Part 1 Chapter 3 Trigonometry - II Ex 3.4 Solution 2 word image 17323 3](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-17323-3.png)
iii. 2cos 4θ cos 2θ = cos(4θ + 2θ)+cos (4θ – 2θ)
= cos 6θ + cos 2θ
iv. 2cos 35° cos75°
= cos(35° + 75°) + cos (35° – 75°)
= cos 110° + cos (-40)°
= cos 110° + cos 40° … [∵ cos(-θ) = cos θ]
Question 2.
Prove the following:
Solution:
![Maharashtra Board Class 11 Maths Part 1 Chapter 3 Trigonometry - II Ex 3.4 Solution 4 word image 17323 6](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-17323-6.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 3 Trigonometry - II Ex 3.4 Solution 5 word image 17323 7](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-17323-7.jpeg)
![Maharashtra Board Class 11 Maths Part 1 Chapter 3 Trigonometry - II Ex 3.4 Solution 6 word image 17323 8](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-17323-8.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 3 Trigonometry - II Ex 3.4 Solution 7 word image 17323 9](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-17323-9.png)
vi. sin 20° sin 40° sin 60° sin 80° = 3/16
Solution: