Question

cos pi/7 +cos 3pi/7 +cos 5pi/7=1/2

Answer 1

Step-by-step explanation:

 cos(π/7) + cos(3π/7) + cos(5π/7)  

Multuiply and divide by 2sin(π/7)  

= 1/2sin(π/7) [ 2sin(π/7)cos(π/7) + 2sin(π/7)cos(3π/7) + 2sin(π/7)cos(5π/7) ]  

Use the following  

sin(2A) = 2sinAcosA  

2sinAcosB = sin(A+B) + sin(A-B)  

= 1/2sin(π/7) [ sin(2π/7) + sin(π/7+3π/7) + sin(π/7-3π/7) + sin(π/7+5π/7) + sin(π/7-5π/7) ]  

= 1/2sin(π/7) [ sin(2π/7) + sin(4π/7) + sin(-2π/7) + sin(6π/7) + sin(-4π/7) ]  

= 1/2sin(π/7) [ sin(2π/7) + sin(4π/7) - sin(2π/7) + sin(6π/7) - sin(4π/7) ]  

= 1/2sin(π/7) [sin(6π/7)]  

= 1/2sin(π/7) [sin(π - π/7)]  

= [sin(π/7)]/2sin(π/7)  

= 1/2

Answer 2

Answer:

1 by 2

Step-by-step explanation:

the solution in above is correct check it from the above one ☺️☺️