Respuesta :

g111319

its a i did this a while ago

mhanifa

Answer:

Lets show that:

  • cos x cos 2x cos 4x cos 8x = sin 16x / 16 sinx

Use formula:

  • sin 2x = 2 sin x cos x

Multiply LHS by 2sinx/2sinx:

  • 2sinx cos x cos 2x cos 4x cos 8x / 2 sin x =
  • sin 2x  cos 2x cos 4x cos 8x / 2 sin x =
  • 2sin 2x cos 2x cos 4x cos 8x / 4 sin x =
  • sin 4x  cos 4x cos 8x / 4 sin x =
  • 2sin 4x  cos 4x cos 8x / 8 sin x =
  • sin 8x cos 8x / 8 sin x =
  • 2 sin 8x cos 8x / 16 sin x =
  • sin 16x / 16 sin x

Now, we can easily find that:

  • sin (16*2π/15) = sin (2π/15)

Coming back to the original equation, we get:

  • cos (2π/15) cos (4π/15) cos (8π/15) cos (16π/15) = sin (16*2π/15) / 16 sin (2π/15)
  • cos (2π/15) cos (4π/15) cos (8π/15) cos (16π/15) = 1/16