Question

prove:cos2π/15cos4π/15cos8π/15cos16π/15=1/16​

Answer 1

Answer:

Step-by-step explanation:

16.cos ( 2π/15).cos (4π/15). cos (8π/15).cos (14π/15)

Divide and multiply by sin 2π/15

16.cos ( 2π/15).cos (4π/15). cos (8π/15).cos (14π/15)

8 ( 2 sin (2π/15)..cos ( 2π/15). cos (4π/15). cos (8π/15).cos (14π/15

=8 sin 4π/15 cos (4π/15). cos (8π/15).cos (14π/15) /sin 2π/15

= 4 * 2sin 4π/15 cos (4π/15).cos (8π/15).cos (14π/15)/sin 2π/15

= 2 * 2 sin (8π/15). cos (8π/15). cos (14π/15)/sin 2π/15

= 2 sin (16π/15).cos (14π/15)/sin 2π/15

= 2sin (π + π/15) * cos ( π - π/15)/sin 2π/15

= ( - 2sin π/15) (-cos π/15)/sin 2π/15

= 2sin (π/15) cos π/15)/sin 2π/15

= sin 2π/15 /sin 2π/15 = 1