Question

hello guys.... ......25 points........

Question: Prove that:- cos 2π/7+cos 4π/7+cos6π/7=-1/2

Maths class 11​

Answer 1

Answer:

[a] sin (π-x) = sin x ----used in step 9  

[b] sin (π+x) = -sin x ----used in step 8  

[c] sin (-x) = -sin x ----used in step 6 (twice)  

[d] sin 2x = 2 sin x cos x ----used in step 4  

[e] sin x cos y = (1/2)sin(x+y) + (1/2)sin(x-y) ----used in step 5 (twice)  

1. cos(2π/7) + cos(4π/7) + cos(6π/7) =  

2. 2sin(2π/7)[(cos(2π/7) + cos(4π/7) + cos(6π/7)] / 2sin(2π/7) =  

3. [2sin(2π/7)cos(2π/7) + 2sin(2π/7)cos(4π/7) + 2sin(2π/7)cos(6π/7)] / 2sin(2π/7) =  

4. [sin(4π/7) + 2sin(2π/7)cos(4π/7) + 2sin(2π/7)cos(6π/7)] / 2sin(2π/7) =  

5. [sin(4π/7) + sin(6π/7) + sin(-2π/7) + sin(8π/7) + sin(-4π/7)] / 2sin(2π/7) =  

6. [sin(4π/7) + sin(6π/7) - sin(2π/7) + sin(8π/7) - sin(4π/7)] / 2sin(2π/7) =  

7. [sin(6π/7) - sin(2π/7) + sin(8π/7)] / 2sin(2π/7) =  

8. [sin(6π/7) - sin(2π/7) - sin(π/7)] / 2sin(2π/7) =  

9. [sin(π/7) - sin(2π/7) - sin(π/7)] / 2sin(2π/7) =  

10. -sin(2π/7) / 2sin(2π/7) =  

11. -1/2

Step-by-step explanation:

Answer 2

Answer:

Answer in attchment dear.......................