Question

5. Prove cos 2π/7. cos 7π/7. cos 8π/7=1/8
​

Answer 1

Answer:

A = cos 3π/7. cos 2π/7. cos π/7  

cos 3π/7 = cos 6π/14 = cos ( π - 8π/14 ) = - cos 8π/14  

Then,  

A = - cos 8π/14. cos 4π/14. cos 2π/14  

= - cos x. cos 2x. cos 4x, ... x = 2π/14  

= (-1/ 2 sin x ). ( 2 sin x. cos x ). cos 2x. cos 4x  

= (-1/ 4 sin x ). ( 2 sin 2x. cos 2x ). cos 4x  

= (-1/ 8 sin x ). ( 2 sin 4x. cos 4x )  

= (-1/8). ( 1 / sin x ). sin 8x  

= (-1/8). ( 1/ sin π/7 ). sin 8π/7  

= (-1/8). ( 1/ sin π/7 ). sin ( π + π/7)  

= (-1/8). ( 1/ sin π/7 ). ( - sin π/7 )  

= 1/8

Step-by-step explanation: